%I #11 Apr 15 2022 10:33:15
%S 1,1,1,2,1,2,1,3,2,3,1,4,1,2,2,5,1,4,1,6,3,3,1,7,2,2,3,4,1,7,1,7,2,3,
%T 2,9,1,2,3,12,1,7,1,6,4,3,1,12,2,6,2,4,1,7,3,7,3,2,1,17,1,3,6,11,2,7,
%U 1,6,2,7,1,16,1,2,4,4,2,7,1,21,5,3,1,16,3,2,3,12,1,16,3,6,2,3,2,19,1,4,4,16,1,7
%N Number of factorizations of the square of n into factors k > 1 for which both A001222(k) and A056239(k) are even.
%C Number of factorizations of n^2 into terms of A340784 that are larger than one.
%H Antti Karttunen, <a href="/A353334/b353334.txt">Table of n, a(n) for n = 1..10080</a>
%H Antti Karttunen, <a href="/A353334/a353334.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A353333(A000290(n)).
%F a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%F a(p) = 1 for all primes p.
%o (PARI)
%o A056239(n) = { my(f); if(1==n, 0, f=factor(n); sum(i=1, #f~, f[i, 2] * primepi(f[i, 1]))); }
%o A353331(n) = ((!(bigomega(n)%2)) && (!(A056239(n)%2)));
%o A353333(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1) && (d<=m) && A353331(d), s += A353333(n/d, d))); (s));
%o A353334(n) = A353333(n^2);
%Y Cf. A000290, A001222, A003961, A056239, A340784, A348717, A353331, A353333.
%Y Differs from A353304 for the first time at n=30, where a(30) = 7, while A353304(30) = 8.
%K nonn
%O 1,4
%A _Antti Karttunen_, Apr 14 2022