Sequences which I have written in the OEIS

 

The OEIS is the best resource for integer sequences on the internet and is maintained and presided over by Neil Sloane with the assistance of an editorial panel of around 70 mathematicians and computer programmers. It currently contains around 200000 sequences, and those listed below are my personal contributions (given in no particular order):

 

 

1.

A126168

Sum of the proper infinitary divisors of n.

 

 

 

2.

A126169

Smaller member of an infinitary amicable pair.

 

 

 

3.

A126170

Larger member of an infinitary amicable pair.

 

 

 

4.

A126171

The number of infinitary amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

5.

A127666

Odd, infinitary abundant numbers.

 

 

 

6.

A127661

Lengths of the infinitary aliquot sequences generated by n.

 

 

 

7.

A126164

Sum of the proper exponential divisors of n.

 

 

 

8.

A126166

Larger member of each exponential amicable pair.

 

 

 

9.

A126173

Larger member of a reduced infinitary amicable pair.

 

 

 

10.

A126174

Smaller member of an augmented infinitary amicable pair.

 

 

 

11.

A126175

Larger member of an augmented infinitary amicable pair.

 

 

 

12.

A126176

Number of augmented infinitary amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

13.

A127667

Odd integers that do not generate monotonically decreasing infinitary aliquot sequences.

 

 

 

14.

A129468

Unitary abundance of the integers.

 

 

 

15.

A111398

Numbers which are the cube roots of the products of their proper divisors.

 

 

 

16.

A126165

The smaller member of each exponential amicable pair.

 

 

 

17.

A127161

Integers whose aliquot sequences terminate by encountering a prime number.

 

 

 

18.

A127162

Composite numbers whose aliquot sequences terminate by encountering a prime number.

 

 

 

19.

A127163

Integers whose aliquot sequences terminate by encountering the prime number 3 (aka the prime family 3).

 

 

 

20.

A127164

Integers whose aliquot sequences terminate by encountering the prime number 7 (aka the prime family 7).

 

 

 

21.

A127656

Lengths of the exponential aliquot sequences.

 

 

 

22.

A127657

Integers whose exponential aliquot sequences end in an e-perfect number.

 

 

 

23.

A127658

Exponential aspiring numbers.

 

 

 

24.

A127659

Exponential amicable numbers.

 

 

 

25.

A127660

Integers whose exponential aliquot sequences end in an exponential amicable pair.

 

 

 

26.

A127662

Integers whose infinitary aliquot sequences end in an infinitary perfect number.

 

 

 

27.

A127663

Infinitary aspiring numbers.

 

 

 

28.

A127664

Infinitary amicable numbers.

 

 

 

29.

A127665

Numbers whose infinitary aliquot sequences end in an infinitary amicable pair (aka the infinitary 2-cycle attractor set).

 

 

 

30.

A126172

The smaller member of a reduced infinitary amicable pair.

 

 

 

31.

A127653

Integers whose unitary aliquot sequences terminate in 0, including 1 but excluding the other trivial cases in which n is itself either a prime or a prime power.

 

 

 

32.

A127654

Unitary aspiring numbers.

 

 

 

33.

A111399

Numbers that are members of A048945 but are not members of A111398.

 

 

 

34.

A128700

Highly abundant numbers with an odd divisor sum.

 

 

 

35.

A129487

Unitary deficient numbers.

 

 

 

36.

A156678

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, gcd (A, B) = 1, A < B<C); sequence gives values of B, sorted to correspond to increasing A (A020884 (n)).

 

 

 

37.

A156679

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, gcd (A, B) = 1, A < B<C); sequence gives values of C, sorted to correspond to increasing A (A020884(n)).

 

 

 

38.

A156681

Consider all Pythagorean triangles A^2 + B^2 = C^2 with A<B<C; sequence gives values of B, sorted to correspond to increasing A (A009004 (n)).

 

 

 

39.

A156682

Consider all Pythagorean triangles A^2 + B^2 = C^2 with A<B<C; sequence gives values of C, sorted to correspond to increasing A (A009004 (n)).

 

 

 

40.

A127652

Integers whose unitary aliquot sequences are longer than their ordinary aliquot sequences.

 

 

 

41.

A128699

Highly abundant numbers that are not superabundant.

 

 

 

42.

A128701

Highly abundant numbers that are not products of consecutive primes with non-increasing exponents, i.e. that are not of the form n=2^{e_2} * 3^{e_3} * ...* p^{e_p}, with e_2>=e_3>=...>=e_p.

 

 

 

43.

A128702

Highly abundant numbers that are not Harshad numbers.

 

 

 

44.

A135928

Digital roots of the Mersenne primes.

 

 

 

45.

A165516

Perfect squares that can be expressed as a sum of three consecutive triangular numbers.

 

 

 

46.

A126104

Numbers n not divisible by 6 such that sigma(n)>3n.

 

 

 

47.

A127655

Numbers whose unitary aliquot sequences end in a unitary amicable pair, but which are not unitary amicable numbers themselves.

 

 

 

48.

A129485

Odd unitary abundant numbers.

 

 

 

49.

A129486

Odd unitary abundant numbers that are not odd, squarefree, ordinary abundant numbers.

 

 

 

50.

A129498

Unitary abundancy of n-th unitary abundant number: usigma(k)-2k if this is >0.

 

 

 

51.

A129499

Records for unitary abundant numbers, i.e. those integers which set a record for having a greater unitary abundance than any of their predecessors.

 

 

 

52.

A129656

Infinitary abundant numbers.

 

 

 

53.

A129657

Infinitary deficient numbers.

 

 

 

54.

A135927

a(n)=a(n-1)^2-2 with a(1)=10. This is the Lucas-Lehmer sequence with starting value 10.

 

 

 

55.

A137716

Number of digits in the n-th Cullen prime.

 

 

 

56.

A156680

Consider primitive Pythagorean triangles (A^2 + B^2 = C^2, gcd (A, B) = 1, A < B<C); sequence gives values of B-A, sorted to correspond to increasing A (A020884 (n)).

 

 

 

57.

A165513

Trapezoidal numbers.

 

 

 

58.

A165514

The complement of the trapezoidal numbers.

 

 

 

59.

A165517

Indices of the least triangular numbers for which three consecutive triangular numbers sum to a perfect square.

 

 

 

60.

A124663

Number of reduced infinitary amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

61.

A126160

Number of betrothed pairs (m,n) with m <=10^k (and k=1,2,3,...), where a betrothed pair satisfies sigma(m)=sigma(n)=m+n+1 and m<n.

 

 

 

62.

A126161

Number of augmented amicable pairs (m,n) with m<n and for which m<=10^k, k=1,2,3,...

 

 

 

63.

A126162

Number of unitary amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

64.

A126163

Number of super unitary amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

65.

A126167

Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.

 

 

 

66.

A129087

Odd, doubly abundant numbers.

 

 

 

67.

A129575

Exponential abundant numbers.

 

 

 

68.

A136188

Digital roots of the Fermat numbers.

 

 

 

69.

A137715

Prime values of k for which k 2^n+1 is composite for all positive integers n.

 

 

 

70.

A137810

a(n)=2^(2^n+n)-1. Such integers are simultaneously Mersenne and Woodall numbers.

 

 

 

71.

A137811

Number of digits in the n-th Woodall prime.

 

 

 

72.

A156683

Integers that can occur as either leg in more than one Pythagorean triple.

 

 

 

73.

A156684

The number of primitive Pythagorean triples A^2+B^2=C^2 with 0 < A < B < C and gcd(A,B)=1, and both legs less than n.

 

 

 

74.

A156685

The number of primitive Pythagorean triples A^2+B^2=C^2 with 0 < A < B < C and gcd(A,B)=1 that have an hypotenuse C that is less than or equal to n.

 

 

 

75.

A156686

The ordered set of a + b - c as (a,b,c) runs through all Pythagorean triples with a<b<c. Also called the excess of a Pythagorean triangle, and is equal to the diameter of its incircle.

 

 

 

76.

A156687

Perimeters of Pythagorean triangles that can be constructed in exactly five different ways.

 

 

 

77.

A156688

The total number of distinct Pythagorean triples with an area numerically equal to n times their perimeters. The members of this sequence are also 1/2 the number of divisors of 8n^2.

 

 

 

78.

A156689

Inradii of primitive Pythagorean triples a^2+b^2=c^2, 0<a<b<c with gcd(a,b)=1, and sorted to correspond to increasing a (given in A020884 ).

 

 

 

79.

A165518

Perfect squares that can be expressed as a sum of four consecutive triangular numbers.

 

 

 

80.

A165519

Integers k for which k(k+1)(k+2) is a triangular number.

 

 

 

81.

A180149

Integers with precisely two partitions into sums of four squares of non-negative numbers.

 

 

 

82.

A180968

The complete set of integers that cannot be partitioned into a sum of six positive squares.

 

 

 

83.

A191759

The units’ digits of the odd square numbers (or the centred octagonal numbers).

 

 

 

84.

A191760

Digital roots of the odd square numbers (or the centred octagonal numbers).

 

 

 

85.

A191761

Units digits of the positive, even squares

 

 

 

86.

A191762

Digital roots of the positive, even squares

 

 

 

87.

A191763

Integers that cannot be partitioned into a sum of an odd square, an even square and a triangular number

 

 

 

88.

A191764

Integers that do not have a partition into a sum of an odd square and two (not necessarily distinct) triangular numbers

 

 

 

89.

A191765

Integers that are a sum of two non-zero triangular numbers and also two non-zero square numbers

 

 

 

90.

A191766

Integers that are a sum of two triangular numbers and two square numbers (including zeros)

 

 

 

91.

A193090

Digital roots of the non-zero pentagonal numbers

 

 

 

92.

A194597

Digital roots of the non-zero hexagonal numbers

 

 

 

93.

A194599

Units digits of the non-zero hexagonal numbers

 

 

 

94.

A194641

Digital roots of the non-zero heptagonal numbers

 

 

 

95.

A194642

Units digits of the non-zero heptagonal numbers

 

 

 

96.

A194731

Digital roots of the non-zero octagonal numbers

 

 

 

97.

A194732

Units digits of the non-zero octagonal numbers

 

 

 

98.

A194825

Digital roots of the non-zero nonagonal numbers

 

 

 

99.

A194826

Units digits of the non-zero nonagonal numbers

 

 

 

100.

A194886

Units digits of the non-zero decagonal numbers

 

 

 

101.

A195527

Integers that are k-gonal for precisely 3 distinct values of k, where k>=3

 

 

 

102.

A195528

Integers that are k-gonal for precisely 4 distinct values of k, where k>=3

 

 

 

103.

A133216

Integers that are simultaneously triangular (A000217) and decagonal (A001107). This sequence began its life as A199086 (defined for natural numbers only), but was subsequently merged with A133216.

 

 

 

104.

A133217

Indices of those triangular numbers (A000217) that are also decagonal (A001107). Similarly, this sequence began its life as A199087 (defined for natural numbers only), but was later merged with A133217.

 

 

 

105.

A133218

Indices of those decagonal numbers (A001107) that are also triangular (A000217). Similarly, this sequence began its life as A199088 (defined for natural numbers only), but was later merged with A133218.

 

 

 

106.

A202563

Numbers which are both decagonal and pentagonal.

 

 

 

107.

A202564

Indices of pentagonal numbers which are also decagonal.

 

 

 

108.

A202565

Indices of decagonal numbers which are also pentagonal.

 

 

 

109.

A203134

Numbers which are both decagonal and hexagonal.

 

 

 

110.

A203135

Indices of hexagonal numbers that are also decagonal.

 

 

 

111.

A203136

Indices of decagonal numbers that are also hexagonal.

 

 

 

112.

A203408

Numbers which are both heptagonal and decagonal.

 

 

 

113.

A203409

Indices of heptagonal numbers that are also decagonal.

 

 

 

114.

A203410

Indices of decagonal numbers that are also heptagonal.

 

 

 

115.

A203624

Numbers which are both decagonal and octagonal.

 

 

 

116.

A203625

Indices of octagonal numbers which are also decagonal.

 

 

 

117.

A203626

Indices of decagonal numbers which are also octagonal.

 

 

 

118.

A203627

Numbers which are both decagonal and nonagonal.

 

 

 

119.

A203628

Indices of nonagonal numbers which are also decagonal.

 

 

 

120.

A203629

Indices of decagonal numbers which are also nonagonal.

 

 

 

121.

A185273

Period 6: repeat (1, 6, 5, 6, 1, 0), or equivalently the units’ digits of the non-zero square triangular numbers.

 

 

 

122.

A205184

Period 12; repeat (1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9)    or equivalently the digital roots of the indices of those non-zero triangular numbers that are also perfect squares.

 

 

 

123.

A205185

Period 6; repeat (1, 8, 9, 8, 1, 0)    or equivalently the units digits of the indices of non-zero triangular numbers that are also perfect squares.

 

 

 

124.

A205650

Period 12; repeat (1, 6, 8, 6, 1, 9, 8, 3, 1, 3, 8, 9)    or equivalently the digital roots of the indices of those non-zero square numbers that are also triangular.

 

 

 

125.

A205651

Period 6; repeat (1, 6, 5, 4, 9, 0)    or equivalently the units’ digits of the indices of those non-zero square numbers that are also triangular.

 

 

 

126.

A213472

Period 20, repeat 1, 4, 0, 9, 1, 6, 4, 5, 9, 6, 6, 9, 5, 4, 6, 1, 9, 0, 4, 1 (or equivalently the units’ digits of the centered triangular numbers A005448(n).

 

 

 

127.

A218324

Odd heptagonal pyramidal numbers A002413(n).

 

 

 

128.

A218325

Even heptagonal pyramidal numbers A002413(n).

 

 

 

129.

A218326

Odd octagonal pyramidal numbers A002414(n).

 

 

 

130.

A218327

Even octagonal pyramidal numbers A002414(n).

 

 

 

131.

A218328

Odd nonagonal pyramidal numbers A007584(n).

 

 

 

132.

A218329

Even nonagonal pyramidal numbers A007584(n).

 

 

 

133.

A218330

Odd decagonal pyramidal numbers A007585(n).

 

 

 

134.

A218331

Even, non-zero decagonal pyramidal numbers A007585(n).

 

 

 

135.

A222882

Decimal expansion of Sierpinski's second constant, K2 = lim_{n->infinity} (1/n * sum(i=1..n, A004018(i^2)) - 4/Pi * log(n)).

 

 

 

136.

A222883

Decimal expansion of Sierpinski's third constant, K3 = lim n->infinity, (1 / n *  sum(i = 1 to n (A004018(i))^2 – 4* log(n)).

 

 

 

137.

A227297

Suppose that (m, m+1) is a pair of consecutive powerful numbers as defined by A001694. This sequence gives the values of m for which neither m nor m+1 are perfect squares.

 

 

 

138.

A228857

Odd primes p>3 for which 14*p+1 is also prime.

 

 

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