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Sum of divisors of 2^prime(n)-1.
2

%I #27 Dec 31 2022 15:06:54

%S 4,8,32,128,2160,8192,131072,524288,8567136,539922240,2147483648,

%T 138055271872,2199187780272,8817412930560,140828559963840,

%U 9008745449302368,576463955735383776,2305843009213693952,147573953351708377936,2361193635521975063040

%N Sum of divisors of 2^prime(n)-1.

%C b-file computed with factorizations in Wagstaff link. a(167) corresponding to 2^991-1 is currently the first unknown term. - _Jens Kruse Andersen_, Sep 28 2014

%C Conjecture: a(n)/2^prime(n) reaches its maximum value 135/128 at n = 5. - _Jianing Song_, Dec 31 2022

%D R. Bojanić, Asymptotic evaluations of the sum of divisors of certain numbers (in Serbo-Croatian), Bull. Soc. Math.-Phys, R.P. Macédoine, Vol. 5 (1954), pp. 5-15.

%D József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 96.

%H Jens Kruse Andersen and Amiram Eldar, <a href="/A247938/b247938.txt">Table of n, a(n) for n = 1..197</a> (terms 1..166 Jens Kruse Andersen)

%H Paul Pollack, <a href="http://pollack.uga.edu/NABDofficial.pdf">Not Always Buried Deep: A Second Course in Elementary Number Theory</a>, AMS, 2009, p. 271, exercise 22.

%H Sam Wagstaff, <a href="http://homes.cerias.purdue.edu/~ssw/cun/">The Cunningham Project</a>.

%F a(n) = A000203(A001348(n)). - _Michel Marcus_, Sep 27 2014

%F Limit_{n->oo} a(n)/A001348(n) = 1 (Bojanić, 1954). - _Amiram Eldar_, Mar 04 2021

%p with(numtheory): A247938:=n->sigma(2^ithprime(n)-1): seq(A247938(n), n=1..20); # _Wesley Ivan Hurt_, Sep 27 2014

%t Table[DivisorSigma[1, 2^Prime[n]-1], {n, 30}]

%o (Magma) [SumOfDivisors(2^p-1): p in PrimesUpTo(100)];

%o (PARI) vector(50,n,sigma(2^prime(n)-1)) \\ _Derek Orr_, Sep 27 2014

%Y Subsequence of A075708.

%Y Cf. A000203, A001348, A034785.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Sep 27 2014