OFFSET
1,1
COMMENTS
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
Conjecture: a(n)/2^prime(n) reaches its maximum value 135/128 at n = 5. - Jianing Song, Dec 31 2022
REFERENCES
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.
József Sándor, Dragoslav S. Mitrinovic and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter III, p. 96.
LINKS
Jens Kruse Andersen and Amiram Eldar, Table of n, a(n) for n = 1..197 (terms 1..166 Jens Kruse Andersen)
Paul Pollack, Not Always Buried Deep: A Second Course in Elementary Number Theory, AMS, 2009, p. 271, exercise 22.
Sam Wagstaff, The Cunningham Project.
FORMULA
Limit_{n->oo} a(n)/A001348(n) = 1 (Bojanić, 1954). - Amiram Eldar, Mar 04 2021
MAPLE
with(numtheory): A247938:=n->sigma(2^ithprime(n)-1): seq(A247938(n), n=1..20); # Wesley Ivan Hurt, Sep 27 2014
MATHEMATICA
Table[DivisorSigma[1, 2^Prime[n]-1], {n, 30}]
PROG
(Magma) [SumOfDivisors(2^p-1): p in PrimesUpTo(100)];
(PARI) vector(50, n, sigma(2^prime(n)-1)) \\ Derek Orr, Sep 27 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Vincenzo Librandi, Sep 27 2014
STATUS
approved