

A307320


a(n) is the base2 logarithm of the denominator of sigma_{1}(P(n)), where P(n) = 2^(n1)*M(n), where M(n) = 2^n  1 is the nth Mersenne number.


0



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
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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



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^(n1)*(2^n1), 1)), 2); \\ Michel Marcus, Apr 02 2019


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



