A075708 - OEIS

%I #29 Jul 02 2024 05:02:55

%S 1,4,8,24,32,104,128,432,592,1536,2160,8736,8192,22528,38912,111456,

%T 131072,473600,524288,1999872,2466048,5909760,8567136,38054016,

%U 34713728,89522176,155493536,462274560,539922240,2015330304,2147483648

%N Sum of the divisors of 2^n - 1.

%C The set {a(n)/(2^n-1)} is dense in [1, oo) (Luca, 2003). - _Amiram Eldar_, Mar 04 2021

%H Amiram Eldar, <a href="/A075708/b075708.txt">Table of n, a(n) for n = 1..1206</a>

%H Paul Erdős, <a href="https://doi.org/10.1007/BF02771618">On the sum Sigma_{d|2^n-1} d^{-1}</a>, Israel Journal of Mathematics, Vol. 9. No. 1 (1971), pp. 43-48; <a href="https://users.renyi.hu/~p_erdos/1971-14.pdf">alternative link</a>.

%H Vaclav Kotesovec, <a href="/A075708/a075708.jpg">Plot of a(n)/((2^n-1)*log(log(n))) for n = 1..1200</a>

%H Florian Luca, <a href="http://dml.cz/dmlcz/129330">On the sum of divisors of the Mersenne numbers</a>, Mathematica Slovaca, Vol. 53. No. 5 (2003), pp. 457-466.

%F a(n) = sigma(2^n - 1).

%F a(n) = A000203(A000225(n)). - _Omar E. Pol_, Dec 08 2019

%F a(n)/(2^n-1) < c * log(log(n)), where c > 0 is a constant (Erdős, 1971). - _Amiram Eldar_, Mar 04 2021

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

%o (PARI) a(n)=sigma(2^n-1) \\ _Charles R Greathouse IV_, Feb 04 2013

%Y Cf. A000203, A000225.

%Y A247938 is a subsequence.

%Y Row sums of A361438.

%K nonn

%O 1,2

%A _Joseph L. Pe_, Oct 03 2002