A173016 Numbers k such that the sequence B = B_k defined by {B(1) = 1; for i >= 2: B(i) = the smallest number h such that sigma(h) = A000203(h) = B(i-1) + k; or B(i) = 0 if no such number h exists} is not the sequence {A063524(j): j >= 1}.

1, 2, 3, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 17, 18, 19, 20, 23, 24, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 47, 48, 53, 54, 55, 56, 57, 59, 60, 61, 62, 63, 67, 68, 71, 72, 73, 74, 77, 78, 79, 80, 83, 84, 89, 90, 91, 92, 93, 95, 96, 97, 98, 101

Offset

1,2

Comments

A063524(n) = characteristic function of 1 = 1,0,0,0,0,0,0,0,0,0,0,0, ...

Numbers k such that A051444(k) and A051444(k+1) are not simultaneously equal to 0.

Complement of A173015.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

a(1) = k = 1 because a_1(n)= A000035(n) = 1,0,1,0,1,0,1,0,1,0,1,0, ...
a(2) = k = 2 because a_2(n)= A173012(n) = 1,2,3,0,0,0,0,0,0,0,0,0, ...
a(3) = k = 3 because a_3(n)= A173013(n) = 1,3,5,7,0,2,0,2,0,2,0,2, ...
a(3) = k = 4 because a_4(n)= A173014(n) = 1,0,3,4,7,0,3,4,7,0,3,4, ...

Mathematica

seq[max_] := Module[{t = Table[1, {max}]}, t[[Complement[Range[max], Table[ DivisorSigma[1, n], {n, 1, max}]]]] = 0; Complement[Range[max - 1], SequencePosition[t, {0, 0}][[;; , 1]]]]; seq[120] (* Amiram Eldar, Mar 22 2024 *)

Crossrefs

Cf. A000035, A000203, A063524, A173012, A173013, A173014, A173015.

Sequence in context: A032847 A023778 A329299 * A053577 A365127 A093515

Adjacent sequences: A173013 A173014 A173015 * A173017 A173018 A173019

Keyword

nonn

Author

Jaroslav Krizek, Nov 06 2010

Extensions

Definition revised by Editors of OEIS, Mar 24 2024

Status

approved