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 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, 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 12 14:45 EDT 2024. Contains 375851 sequences. (Running on oeis4.)