A112965 a(n) = Sum_{i+j=n} omega(i)*omega(j), where omega = A001221.

0, 0, 0, 1, 2, 3, 4, 7, 8, 9, 10, 14, 14, 17, 18, 23, 24, 27, 26, 32, 32, 35, 36, 44, 42, 47, 48, 52, 50, 58, 54, 65, 62, 67, 66, 78, 70, 79, 78, 88, 84, 94, 88, 100, 100, 103, 100, 118, 106, 119, 114, 124, 116, 135, 122, 138, 134, 141, 136, 155, 142, 155, 154, 163, 156

Offset: 1

Author

Reinhard Zumkeller, Oct 07 2005

Keywords

• nonn

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A013939, A112966, A112967.

Programs

Mathematica

Table[Sum[PrimeNu[i]*PrimeNu[n - i], {i, n - 1}], {n, 65}] (* Ivan Neretin, Jan 21 2017 *)

PARI

a(n) = sum(i=2, n-2, omega(i)*omega(n-i)); \\ Michel Marcus, Jan 22 2017

Formula

G.f.: (Sum_{k>=1} x^prime(k)/(1 - x^prime(k)))^2. - Ilya Gutkovskiy, Jan 31 2017