OFFSET
1,2
COMMENTS
Lim_{n->oo} a(n) = oo because a(n) > sqrt(prime(n)) [see the reference], but this sequence is not monotone increasing.
a(n) is the sum of aliquot parts of the sum of divisors of n-th prime (see Marcus's formula). - Omar E. Pol, Apr 18 2020
REFERENCES
J.-M. De Koninck & A. Mercier, 1001 Problèmes en Théorie Classique des Nombres, Problème 617 pp. 82, 280, Ellipses, Paris, 2004.
FORMULA
EXAMPLE
As prime(6) = 13, a(6) = sigma(14) - sigma(13) = 24 - 14 = 10.
MAPLE
G:= seq(sigma(ithprime(p)+1)-sigma(ithprime(p)), p=1..200);
MATHEMATICA
(DivisorSigma[1, # + 1] - # - 1)& @ Select[Range[300], PrimeQ] (* Amiram Eldar, Apr 18 2020 *)
PROG
(PARI) a(n) = my(p=prime(n)); sigma(p+1) - (p+1); \\ Michel Marcus, Apr 18 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 18 2020
STATUS
approved