OFFSET
1,1
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
Equals M * V, where M = A127093 as an infinite lower triangular matrix and V = A000040, the sequence of primes as a vector. E.g., a(4) = 36 = 1*2 + 2*3 + 4*7, where (1, 2, 0, 4) = row 4 of A127093 and 2, 3 and 7 are p(1), p(2), p(4). - Gary W. Adamson, Jan 11 2007
L.g.f.: log(Product_{k>=1} 1/(1 - x^k)^prime(k)) = Sum_{n>=1} a(n)*x^n/n. - Ilya Gutkovskiy, May 10 2017
EXAMPLE
a(4)=36 because the divisors of 4 are 1,2,4 and 1*p(1) + 2*p(2) + 4*p(4) = 1*2 + 2*3 + 4*7 = 36.
MAPLE
with(numtheory): a:=proc(n) local div: div:=divisors(n): sum(div[j]*ithprime(div[j]), j=1..tau(n)) end: seq(a(n), n=1..55); # Emeric Deutsch, Jan 20 2007
PROG
(PARI) a(n) = sumdiv(n, d, d*prime(d)); \\ Michel Marcus, Jun 24 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 16 2001
EXTENSIONS
Edited by N. J. A. Sloane, May 04 2007
STATUS
approved