A353338 - OEIS

A353338

Number of ways to write the square of n as a product of the terms of A028260 larger than 1; a(1) = 1 by convention (an empty product).

1, 1, 1, 2, 1, 3, 1, 3, 2, 3, 1, 6, 1, 3, 3, 5, 1, 6, 1, 6, 3, 3, 1, 12, 2, 3, 3, 6, 1, 12, 1, 7, 3, 3, 3, 16, 1, 3, 3, 12, 1, 12, 1, 6, 6, 3, 1, 21, 2, 6, 3, 6, 1, 12, 3, 12, 3, 3, 1, 33, 1, 3, 6, 11, 3, 12, 1, 6, 3, 12, 1, 33, 1, 3, 6, 6, 3, 12, 1, 21, 5, 3, 1, 33, 3, 3, 3, 12, 1, 33, 3, 6, 3, 3, 3, 36, 1, 6, 6

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OFFSET

1,4

COMMENTS

Number of factorizations of n^2 into factors k > 1 for which there is an even number of primes (when counted with multiplicity, A001222) in their prime factorization.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = A353337(A000290(n)).

a(n) = a(A046523(n)). [The sequence depends only on the prime signature of n].

For all n >= 1, a(n) >= A353378(n).

PROG

(PARI)

A065043(n) = (1 - (bigomega(n)%2));

A353337(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&A065043(d), s += A353337(n/d, d))); (s));

A353338(n) = A353337(n^2);