%I #19 Jun 24 2018 08:59:07

%S 2,8,17,36,57,101,121,188,224,353,343,573,535,729,777,1036,1005,1406,

%T 1275,1801,1669,2087,1911,2861,2482,3167,3005,3753,3163,4541,3939,

%U 5228,4879,5737,5391,7314,5811,7475,7063,8873,7341,9957,8215,10607,9849

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

%H Seiichi Manyama, <a href="/A061150/b061150.txt">Table of n, a(n) for n = 1..10000</a>

%F 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

%F 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

%e 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.

%p 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

%o (PARI) a(n) = sumdiv(n, d, d*prime(d)); \\ _Michel Marcus_, Jun 24 2018

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

%Y Cf. A127093.

%K easy,nonn

%O 1,1

%A _Vladeta Jovovic_, Apr 16 2001

%E Edited by _N. J. A. Sloane_, May 04 2007