A075708 Sum of the divisors of 2^n - 1.

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

Offset: 1

Author

Joseph L. Pe, Oct 03 2002

Keywords

• nonn

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 of 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.

Crossrefs

Cf. A000203, A000225.

A247938 is a subsequence.

Row sums of A361438.

Programs

Mathematica

Table[DivisorSigma[1, 2^n - 1], {n, 1, 40}]

PARI

a(n)=sigma(2^n-1) \\ Charles R Greathouse IV, Feb 04 2013

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