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A307320
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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.
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0
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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
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1,6
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COMMENTS
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a(n) = 0 if and only if P(n) is multiperfect. In particular, a(n) = 0 if M(n) is prime.
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LINKS
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EXAMPLE
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a(6) = 2 since P(6) = 2016 and sigma_{-1}(2016) = 13/2^2.
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MATHEMATICA
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M[n_] := 2^n - 1;
P[n_] := 2^(n - 1) M[n];
A[n_] := Log[2, Denominator[DivisorSigma[-1, P[n]]]];
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PROG
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(PARI) a(n) = logint(denominator(sigma(2^(n-1)*(2^n-1), -1)), 2); \\ Michel Marcus, Apr 02 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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