A345344 - OEIS

%I #11 Jun 16 2021 04:17:59

%S 0,1,1,2,1,2,1,4,2,2,1,4,1,2,2,6,1,4,1,4,2,2,1,6,2,2,4,4,1,3,1,9,2,2,

%T 2,8,1,2,2,6,1,3,1,4,4,2,1,9,2,4,2,4,1,6,2,6,2,2,1,6,1,2,4,12,2,3,1,4,

%U 2,3,1,12,1,2,4,4,2,3,1,9,6,2,1,6,2,2,2,6,1,6,2,4,2

%N a(n) = Sum_{d^2|n} Omega(n/d^2).

%F a(p) = Sum_{d^2|p} Omega(p/d^2) = Omega(p) = 1 for primes p.

%e a(24) = Sum_{d^2|24} Omega(24/d^2) = Omega(24) + Omega(6) = 4 + 2 = 6.

%e a(32) = Sum_{d^2|32} Omega(32/d^2) = Omega(32) + Omega(8) + Omega(2) = 5 + 3 + 1 = 9.

%t Table[Sum[PrimeOmega[n/k^2] (1 - Ceiling[n/k^2] + Floor[n/k^2]), {k, n}], {n, 100}]

%o (PARI) a(n) = sumdiv(n, d, if (issquare(d), bigomega(n/d))); \\ _Michel Marcus_, Jun 14 2021

%Y Cf. A001222 (Omega), A345345.

%K nonn

%O 1,4

%A _Wesley Ivan Hurt_, Jun 14 2021