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

Author

David Terr, Apr 02 2019

Keywords

• nonn

Comments

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

Examples

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

Programs

Mathematica

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

PARI

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

Extensions

More terms from Felix Fröhlich, Sep 29 2019