A382966 The number of non-unitary prime divisors of the n-th biquadratefree number that is not cubefree.

1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1

Offset

1,7

Links

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

Formula

a(n) = A056170(A375072(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = ((1/zeta(4)) * Sum_{p prime} (1/(p^2+1)) - (1/zeta(3)) * Sum_{p prime} ((p-1)/(p^3-1))) / (1/zeta(4) - 1/zeta(3)) = 1.20757893653588072073... .

Mathematica

f[k_] := If[k == 1, Nothing, Module[{e = FactorInteger[k][[;; , 2]]}, If[Max[e] == 3, Count[e, _?(# > 1 &)], Nothing]]]; Array[f, 1000]

Prog

(PARI) list(lim) = {my(e); for(k = 2, lim, e = factor(k)[, 2]; if(vecmax(e) == 3, print1(#select(x -> x > 1, e), ", "))); }

Crossrefs

Cf. A002117, A013662, A056170, A375072, A376366, A382425, A382965, A382968.

Sequence in context: A097588 A183017 A183014 * A030382 A354614 A192004

Adjacent sequences: A382963 A382964 A382965 * A382967 A382968 A382969

Keyword

nonn,easy

Author

Amiram Eldar, Apr 10 2025

Status

approved