A061150 a(n) = Sum_{d|n} d*prime(d).

2, 8, 17, 36, 57, 101, 121, 188, 224, 353, 343, 573, 535, 729, 777, 1036, 1005, 1406, 1275, 1801, 1669, 2087, 1911, 2861, 2482, 3167, 3005, 3753, 3163, 4541, 3939, 5228, 4879, 5737, 5391, 7314, 5811, 7475, 7063, 8873, 7341, 9957, 8215, 10607, 9849

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

Cf. A007441, A007445, A030009, A061151-A061152.

Cf. A127093.

Sequence in context: A034972 A294537 A294548 * A160189 A281470 A295147

Adjacent sequences: A061147 A061148 A061149 * A061151 A061152 A061153

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 16 2001

Extensions

Edited by N. J. A. Sloane, May 04 2007

Status

approved