A341353 Greatest k such that 3^k divides A156552(n); the 3-adic valuation of A156552(n).

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, 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, 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

Offset: 2

Author

Antti Karttunen, Feb 14 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65539
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

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

Programs

PARI

A007949(n) = valuation(n,3);
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 };
A341353(n) = A007949(A156552(n));

Formula

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

a(p) = 0 for all primes p.

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

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