A368711 The maximal exponent in the prime factorization of the exponentially odd numbers (A268335).

0, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1

Offset: 1

Author

Amiram Eldar, Jan 04 2024

Keywords

• nonn
• easy

Comments

Differs from A368472 at n = 1, 154, 610, 707, 762, ... .

Links

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

Crossrefs

Cf. A033150, A051903, A268335, A368472.

Similar sequences: A368710, A368712, A368713.

Programs

Mathematica

f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[AllTrue[e, OddQ], Max @@ e, Nothing]]; f[1] = 0; Array[f, 150]

PARI

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

Formula

a(n) = A051903(A268335(n)).

a(n) is odd for n >= 2.

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + 2 * Sum_{k>=1} (1 - Product_{p prime} (1 - 1/(p^(2*k-1)*(p^2+p-1)))) = 1.34877064483679975726... .