A368472 Product of exponents of prime factorization of the exponentially odd numbers.

1, 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

The odd terms of A005361.

The first position of 2*k-1, for k = 1, 2, ..., is 1, 7, 24, 91, 154, 1444, 5777, 610, 92349, ..., which is the position of A085629(2*k-1) in A268335.

Links

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

Formula

a(n) = A005361(A268335(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (zeta(2)^2/d) * Product_{p prime} (1 - 3/p^2 + 3/p^3 - 1/p^5) = 1.38446562720473484463..., where d = A065463 is the asymptotic density of the exponentially odd numbers.

Mathematica

f[n_] := Module[{p = Times @@ FactorInteger[n][[;; , 2]]}, If[OddQ[p], p, Nothing]]; Array[f, 150]

Prog

(PARI) lista(kmax) = {my(p); for(k = 1, kmax, p = vecprod(factor(k)[, 2]); if(p%2, print1(p, ", "))); }

Crossrefs

Cf. A005361, A013661, A065463, A085629, A098198, A268335.

Cf. A366438, A366439.

Similar sequences: A322327, A368473, A368474.

Sequence in context: A030577 A070670 A372466 * A368711 A380325 A049586

Adjacent sequences: A368469 A368470 A368471 * A368473 A368474 A368475

Keyword

nonn,easy

Author

Amiram Eldar, Dec 26 2023

Status

approved