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 A075708 Sum of the divisors of 2^n - 1. 7
 1, 4, 8, 24, 32, 104, 128, 432, 592, 1536, 2160, 8736, 8192, 22528, 38912, 111456, 131072, 473600, 524288, 1999872, 2466048, 5909760, 8567136, 38054016, 34713728, 89522176, 155493536, 462274560, 539922240, 2015330304, 2147483648 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The set {a(n)/(2^n-1)} is dense in [1, oo) (Luca, 2003). - Amiram Eldar, Mar 04 2021 LINKS Amiram Eldar, Table of n, a(n) for n = 1..1206 Paul Erdős, On the sum Sigma_{d|2^n-1} d^{-1}, Israel Journal of Mathematics, Vol. 9. No. 1 (1971), pp. 43-48; alternative link. Vaclav Kotesovec, Plot a(n)/((2^n-1)*log(log(n))) for n = 1..1200 Florian Luca, On the sum of divisors of the Mersenne numbers, Mathematica Slovaca, Vol. 53. No. 5 (2003), pp. 457-466. FORMULA a(n) = sigma(2^n - 1). a(n) = A000203(A000225(n)). - Omar E. Pol, Dec 08 2019 a(n)/(2^n-1) < c * log(log(n)), where c > 0 is a constant (Erdős, 1971). - Amiram Eldar, Mar 04 2021 MATHEMATICA Table[DivisorSigma[1, 2^n - 1], {n, 1, 40}] PROG (PARI) a(n)=sigma(2^n-1) \\ Charles R Greathouse IV, Feb 04 2013 CROSSREFS Cf. A000203, A000225. A247938 is a subsequence. Sequence in context: A254731 A291548 A212019 * A066617 A272272 A024589 Adjacent sequences:  A075705 A075706 A075707 * A075709 A075710 A075711 KEYWORD nonn AUTHOR Joseph L. Pe, Oct 03 2002 STATUS approved

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Last modified January 26 09:29 EST 2022. Contains 350597 sequences. (Running on oeis4.)