A307320 a(n) is the base-2 logarithm of the denominator of sigma_{-1}(P(n)), where P(n) = 2^(n-1)*M(n), where M(n) = 2^n - 1 is the n-th Mersenne number.

0, 0, 0, 0, 0, 2, 0, 3, 4, 0, 6, 6, 0, 2, 3, 10, 0, 8, 0, 9, 12, 13, 17, 16, 17, 8, 21, 13, 22, 14, 0, 25, 22, 12, 18, 22, 30, 14, 17, 27, 36, 29, 32, 32, 25, 36, 40, 37, 40, 34, 18, 30, 47, 44, 40, 39, 29, 46, 53, 40, 0, 26, 51, 55, 41, 50, 62, 42, 57, 44, 61

Offset

1,6

Comments

a(n) = 0 if and only if P(n) is multiperfect. In particular, a(n) = 0 if M(n) is prime.

Links

Table of n, a(n) for n=1..71.

Example

a(6) = 2 since P(6) = 2016 and sigma_{-1}(2016) = 13/2^2.

Mathematica

M[n_] := 2^n - 1;
P[n_] := 2^(n - 1) M[n];
A[n_] := Log[2, Denominator[DivisorSigma[-1, P[n]]]];

Prog

(PARI) a(n) = logint(denominator(sigma(2^(n-1)*(2^n-1), -1)), 2); \\ Michel Marcus, Apr 02 2019

Crossrefs

Sequence in context: A091538 A340991 A013584 * A350227 A137372 A212844

Adjacent sequences: A307317 A307318 A307319 * A307321 A307322 A307323

Keyword

nonn

Author

David Terr, Apr 02 2019

Extensions

More terms from Felix Fröhlich, Sep 29 2019

Status

approved