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

1,7

Comments

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

Links

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

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... .

Mathematica

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

Prog

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

Crossrefs

Cf. A033150, A051903, A268335, A368472.

Similar sequences: A368710, A368712, A368713.

Sequence in context: A070670 A372466 A368472 * A049586 A342466 A133721

Adjacent sequences: A368708 A368709 A368710 * A368712 A368713 A368714

Keyword

nonn,easy

Author

Amiram Eldar, Jan 04 2024

Status

approved