A023567 Convolution of A023531 and primes.

0, 2, 3, 5, 9, 14, 18, 24, 32, 39, 51, 57, 71, 85, 94, 108, 124, 142, 152, 176, 193, 205, 229, 249, 271, 295, 315, 336, 364, 386, 408, 444, 468, 490, 526, 561, 583, 617, 663, 681, 717, 745, 781, 831, 862, 894, 924, 968, 1006, 1050, 1100, 1138, 1174

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Programs

Maple

Primes:= select(isprime, [2,seq(i,i=3..1000,2)]):
seq(add(Primes[n - i*(i+3)/2],i=1..floor((sqrt(1+8*n)-3)/2)), n=2..nops(Primes)); # Robert Israel, Dec 28 2015

PARI

vector(20,x,c=0;j=x;t=3;while(j>1,c+=prime(j-1);j-=t;t+=1);c)

Formula

a(n) = Sum_{i=0..n-1} A023531(n-i)*p(i+1) where p(i) is the i-th prime.

Extensions

Corrected (term 781 was missing) by Jeremy Gardiner, Feb 05 2014