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a(n) = Product_{p|n, p<n} omega(n/p).
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%I #43 Jul 10 2020 09:42:00

%S 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,2,1,2,1,1,1,2,1,1,1,2,1,8,1,1,1,1,

%T 1,4,1,1,1,2,1,8,1,2,2,1,1,2,1,2,1,2,1,2,1,2,1,1,1,12,1,1,2,1,1,8,1,2,

%U 1,8,1,4,1,1,2,2,1,8,1,2,1,1,1,12,1,1,1,2,1,12,1,2,1

%N a(n) = Product_{p|n, p<n} omega(n/p).

%F If n > 1 is squarefree and composite, then a(n) = (omega(n)-1)^omega(n).

%F If n = p^k where p is prime and k is a nonnegative integer, then a(n) = 1.

%t Table[Product[PrimeNu[n/i]^((PrimePi[i] - PrimePi[i - 1])*(1 - Ceiling[n/i] + Floor[n/i])), {i, n - 1}], {n, 100}]

%o (PARI) a(n) = my(f=factor(n)[,1]); prod(k=1, #f~, if (f[k] < n, omega(n/f[k]), 1)); \\ _Michel Marcus_, Jun 09 2020

%Y Cf. A001221 (omega).

%K nonn,easy

%O 1,12

%A _Wesley Ivan Hurt_, Jun 09 2020