A341353 - OEIS

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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

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OFFSET

2,9

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..65539

Index entries for sequences computed from indices in prime factorization

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.

PROG

(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));

CROSSREFS

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

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

Sequence in context: A080224 A341508 A261488 * A010105 A341618 A337690

Adjacent sequences: A341350 A341351 A341352 * A341354 A341355 A341356

KEYWORD

nonn

AUTHOR

Antti Karttunen, Feb 14 2021

STATUS

approved