Amiram Eldar, <a href="/A368039/b368039_1.txt">Table of n, a(n) for n = 1..10000</a>

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OEIS Server: Installed first b-file as b368039.txt.

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Amiram Eldar, <a href="/A368039/b368039_1.txt">Table of n, a(n) for n = 1..10000</a>

allocatedThe product of exponents of prime factorization of forthe Amiramnonsquarefree Eldarnumbers.

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

1,1

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

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... .

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

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

Cf. A005117, A005361, A013929.

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

Cf. A059956, A082695, A229099.

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Amiram Eldar, Dec 09 2023

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