A368541 The number of exponential divisors of the nonsquarefree numbers.

2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 4, 2, 4, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 6, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 4, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 2, 4, 2, 2, 4, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 4, 4, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 4, 3

Offset

1,1

Comments

The terms of A049419 that are larger than 1, since A049419(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) = A049419(A013929(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (A327837 - A059956)/A229099 = 2.53623753427906735929... .

Mathematica

f[p_, e_] := DivisorSigma[0, e]; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 200], # > 1 &]

Prog

(PARI) lista(kmax) = {my(p, f); for(k = 1, kmax, f = factor(k); p = prod(i=1, #f~, numdiv(f[i, 2])); if(p > 1, print1(p, ", "))); }

Crossrefs

Cf. A005117, A013929, A049419.

Cf. A084936, A174961, A275699, A368038, A368039, A368040.

Cf. A013661, A059956, A229099, A327837.

Sequence in context: A368876 A270616 A304523 * A020649 A362366 A183024

Adjacent sequences: A368538 A368539 A368540 * A368542 A368543 A368544

Keyword

nonn

Author

Amiram Eldar, Dec 29 2023

Status

approved