A368039 The product of exponents of prime factorization of the nonsquarefree numbers.

2, 3, 2, 2, 4, 2, 2, 3, 2, 3, 2, 5, 4, 3, 2, 2, 4, 2, 2, 2, 3, 3, 2, 2, 6, 2, 6, 2, 2, 4, 4, 2, 3, 2, 2, 5, 2, 2, 4, 3, 6, 4, 2, 2, 3, 2, 2, 3, 2, 7, 2, 3, 3, 2, 8, 2, 2, 2, 3, 2, 2, 5, 4, 2, 3, 2, 2, 2, 2, 4, 4, 3, 2, 3, 6, 4, 2, 6, 2, 2, 4, 2, 9, 2, 5, 4, 2

Offset

1,1

Comments

The terms of A005361 that are larger than 1, since A005361(k) = 1 if and only if k is squarefree (A005117).

Links

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

Formula

a(n) = A005361(A013929(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = ((zeta(2)*zeta(3)/zeta(6)) - 1/zeta(2))/(1-1/zeta(2)) = (A082695 - A059956)/A229099 = 3.406686208821... .

Mathematica

Select[Table[Times @@ FactorInteger[n][[;; , 2]], {n, 1, 250}], # > 1 &]

Prog

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

Crossrefs

Cf. A005117, A005361, A013929.

Cf. A084936, A174961, A275699, A368038, A368040.

Cf. A059956, A082695, A229099.

Sequence in context: A295312 A212174 A368713 * A160558 A241019 A023581

Adjacent sequences: A368036 A368037 A368038 * A368040 A368041 A368042

Keyword

nonn

Author

Amiram Eldar, Dec 09 2023

Status

approved