A275478 Least k such that d(n) divides d(n+2^k) (d = A000005).

0, 0, 1, 3, 0, 1, 0, 1, 4, 2, 0, 3, 0, 0, 7, 5, 0, 1, 0, 3, 0, 1, 0, 4, 7, 0, 3, 2, 0, 8, 0, 6, 0, 0, 2, 6, 0, 0, 0, 1, 0, 7, 0, 0, 23, 3, 0, 5, 0, 1, 2, 3, 0, 1, 0, 5, 0, 1, 0, 9, 0, 2, 9, 7, 0, 2, 0, 2, 0, 3, 0, 7, 0, 2, 0, 3, 0, 5, 0, 5, 178, 1, 0, 8, 0, 0, 0, 4, 0, 24, 1, 2, 0, 0, 0, 6, 0, 0, 20, 9

Offset: 1

Author

Altug Alkan, Jul 29 2016

Keywords

• nonn

Comments

a(225) > 300, if it exists. - Antti Karttunen, Jun 13 2023

Examples

			a(45) = 23 because A000005(45) = 6 divides A000005(45+2^23) = 18.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..224

Crossrefs

Cf. A000005, A057922, A275473, A275479.

Programs

Mathematica

A275478[n_]:=Module[{d=DivisorSigma[0,n],k=-1},While[!Divisible[DivisorSigma[0,n+2^++k],d]];k];Array[A275478,50] (* Paolo Xausa, Aug 13 2023 *)

PARI

a(n) = {my(k = 0); while(numdiv(n+2^k) % numdiv(n) != 0, k++); k; }

Formula

a(A057922(n)) = 0. - Michel Marcus, Aug 01 2016

Extensions

Data section extended up to a(100) by Antti Karttunen, Mar 02 2023