%I #16 Mar 18 2022 00:30:31

%S 0,0,0,1,0,2,0,1,1,2,0,3,0,2,2,1,0,3,0,3,2,2,0,3,1,2,1,3,0,6,0,1,2,2,

%T 2,4,0,2,2,3,0,6,0,3,3,2,0,3,1,3,2,3,0,3,2,3,2,2,0,7,0,2,3,1,2,6,0,3,

%U 2,6,0,4,0,2,3,3,2,6,0,3,1,2,0,7,2,2,2,3,0,7,2,3

%N a(n) = Sum_{p|n, p prime} omega(n/p).

%F a(p) = 0 for p prime.

%F a(n) = Sum_{a*b*c=n} omega(a)*omega(b)*mu(c). - _Benedict W. J. Irwin_, Mar 02 2022

%e a(30) = Sum_{p|30} omega(30/p) = omega(15) + omega(10) + omega(6) = 2 + 2 + 2 = 6.

%t Table[Sum[PrimeNu[n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

%o (PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, omega(n/f[k,1])); \\ _Michel Marcus_, Jun 16 2021

%Y Cf. A001221 (omega).

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Jun 15 2021