cp's OEIS Frontend

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).

%I A353338 #11 Apr 19 2022 11:41:09
%S A353338 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,
%T A353338 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,
%U A353338 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
%N 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).
%C A353338 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.
%H A353338 Antti Karttunen, <a href="/A353338/b353338.txt">Table of n, a(n) for n = 1..16384</a>
%H A353338 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A353338 a(n) = A353337(A000290(n)).
%F A353338 a(n) = a(A046523(n)). [The sequence depends only on the prime signature of n].
%F A353338 For all n >= 1, a(n) >= A353378(n).
%o A353338 (PARI)
%o A353338 A065043(n) = (1 - (bigomega(n)%2));
%o A353338 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));
%o A353338 A353338(n) = A353337(n^2);
%Y A353338 Cf. A000290, A001222, A028260, A038548, A046523, A065043, A353337.
%Y A353338 Cf. also A353378.
%K A353338 nonn
%O A353338 1,4
%A A353338 _Antti Karttunen_, Apr 17 2022