A358266 Numbers k such that the aliquot sequence of 2^k ends with the prime 7.

3, 10, 12, 141, 278, 387, 421

Offset

1,1

Links

Table of n, a(n) for n=1..7.

Jean-Luc Garambois, Aliquot sequences starting on integer powers n^i, n^i project.

Mersenne forum, n^i project.

Formula

Define s(i) = sigma(i) - i = A000203(i) - i. Then k is a term of this sequence if the aliquot sequence obtained by repeatedly applying the mapping i->s(i) taking as initial value 2^k terminates in the prime 7.

Example

a(4)=141 because the aliquot sequence that starts with the integer 2^141 ends with the prime number 7 and there are only three smaller powers of 2 that do the same: 2^3, 2^10 and 2^12.

Prog

(PARI) f(n) = if (n==1, return(2)); my(list = List(), s=2^n); for (i=1, oo, s = sigma(s) - s; if (#select(x->(x==s), list), return(0)); if (isprime(s), return (s)); listput(list, s); );
isok(m) = f(m) == 7;

Crossrefs

Cf. A127164, A358239.

Sequence in context: A032916 A044994 A242900 * A299403 A174242 A022415

Adjacent sequences: A358263 A358264 A358265 * A358267 A358268 A358269

Keyword

nonn,hard,more

Author

Jean Luc Garambois, Nov 06 2022

Status

approved