cp's OEIS Frontend

A353304 Number of factorizations of n^2 into factors k > 1 for which A156552(k) is a multiple of three.

%I A353304 #11 Apr 11 2022 20:48:44
%S A353304 1,1,1,2,1,2,1,3,2,3,1,4,1,2,2,5,1,4,1,6,3,3,1,7,2,2,3,4,1,8,1,7,2,3,
%T A353304 2,9,1,2,3,12,1,7,1,6,4,3,1,12,2,6,2,4,1,7,3,7,3,2,1,19,1,3,6,11,2,8,
%U A353304 1,6,2,7,1,16,1,2,4,4,2,7,1,21,5,3,1,16,3,2,3,12,1,18,3,6,2,3,2,19,1,4,4,16,1,8
%N A353304 Number of factorizations of n^2 into factors k > 1 for which A156552(k) is a multiple of three.
%C A353304 Number of factorizations of the square of n into terms of A329609 that are larger than one.
%H A353304 Antti Karttunen, <a href="/A353304/b353304.txt">Table of n, a(n) for n = 1..10080</a>
%H A353304 Antti Karttunen, <a href="/A353304/a353304.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%H A353304 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A353304 a(n) = A353303(A000290(n)).
%F A353304 a(p) = 1 for all primes p.
%F A353304 a(n) = a(A003961(n)) = a(A348717(n)), for all n >= 1.
%o A353304 (PARI)
%o A353304 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A353304 A353269(n) = (!(A156552(n)%3));
%o A353304 A353303(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((d>1)&&(d<=m)&&
%o A353304 A353269(d), s += A353303(n/d, d))); (s));
%o A353304 A353304(n) = A353303(n^2);
%Y A353304 Cf. A000290, A003961, A156552, A329609, A348717, A353269, A353303.
%K A353304 nonn
%O A353304 1,4
%A A353304 _Antti Karttunen_, Apr 10 2022