A374324 The maximal exponent in the prime factorization of the numbers whose maximal exponent in their prime factorization is even.

0, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 6, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 2, 2, 6, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 8, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A051903(A368714(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{k>=1} (2*k * (1/zeta(2*k+1) - 1/zeta(2*k))) / Sum_{k>=2} (-1)^k * (1 - 1/zeta(k)) = 2.48584683692026915946... .

Mathematica

f[n_] := Module[{e = If[n == 1, 0, Max[FactorInteger[n][[;; , 2]]]]}, If[EvenQ[e], e, Nothing]]; Array[f, 350]

Prog

(PARI) lista(kmax) = {my(e); print1(0, ", "); for(k = 2, kmax, e = vecmax(factor(k)[, 2]); if(!(e % 2), print1(e, ", "))); }

Crossrefs

Cf. A051903, A368714.

Similar sequences: A374325, A374326, A374327, A374328.

Sequence in context: A138260 A027389 A337539 * A111735 A211454 A242310

Adjacent sequences: A374321 A374322 A374323 * A374325 A374326 A374327

Keyword

nonn,easy

Author

Amiram Eldar, Jul 04 2024

Status

approved