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 A345345 a(n) = Sum_{d^2|n} omega(n/d^2). 1

%I

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

%T 2,4,1,2,2,4,1,3,1,3,3,2,1,5,1,3,2,3,1,4,2,4,2,2,1,5,1,2,3,3,2,3,1,3,

%U 2,3,1,6,1,2,3,3,2,3,1,5,2,2,1,5,2,2,2,4,1,5,2,3

%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 p prime.

%e a(12) = Sum_{d^2|12} omega(12/d^2) = omega(12) + omega(3) = 2 + 1 = 3.

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

%t 100}]

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

%Y Cf. A001221 (omega), A062799, A345344.

%K nonn

%O 1,6

%A _Wesley Ivan Hurt_, Jun 14 2021

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Last modified January 17 16:58 EST 2022. Contains 350402 sequences. (Running on oeis4.)