A334933 - OEIS

A334933

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

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, 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, 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

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OFFSET

1,12

LINKS

Table of n, a(n) for n=1..93.

FORMULA

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

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

MATHEMATICA

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

PROG

(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