%I #12 Feb 15 2021 22:50:20

%S 0,0,1,0,0,0,0,1,2,0,0,0,0,0,1,0,0,0,0,2,1,0,0,1,0,0,0,0,1,0,0,0,1,0,

%T 3,0,0,1,1,0,0,0,0,0,3,0,0,1,0,0,0,0,0,2,0,1,0,0,0,0,1,0,2,0,1,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,0,3,3,0,2,2,0,0,2,0,0,0,0,0,1,0,2,0,0

%N Greatest k such that 3^k divides A156552(n); the 3-adic valuation of A156552(n).

%H Antti Karttunen, <a href="/A341353/b341353.txt">Table of n, a(n) for n = 2..65539</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A007949(A156552(n)).

%F a(p) = 0 for all primes p.

%F a(n^2) > 0 for all n >= 2.

%F a(n) > 0 iff A329903(n) = 0.

%o (PARI)

%o A007949(n) = valuation(n,3);

%o A156552(n) = { my(f = factor(n), 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 A341353(n) = A007949(A156552(n));

%Y Cf. A007949, A156552, A329609 (positions of nonzeros), A329903, A341354 (even bisection), A341355.

%Y Cf. also A055396 (the 2-adic valuation + 1), A292251.

%K nonn

%O 2,9

%A _Antti Karttunen_, Feb 14 2021