A382968 The number of non-unitary prime divisors of the n-th biquadratefree number that is not squarefree.

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

Offset

1,11

Links

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

Formula

a(n) = A056170(A382967(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (15/(15-Pi^2)) * Sum_{p prime} (1/(p^2+1)) = 1.13751331982931014416... .

Mathematica

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

Prog

(PARI) list(lim) = {my(e, emax); for(k = 2, lim, e = factor(k)[, 2]; emax = vecmax(e); if(emax > 1 && emax < 4, print1(#select(x -> x > 1, e), ", "))); }

Crossrefs

Cf. A056170, A382425, A382965, A382966, A382967.

Sequence in context: A043285 A353756 A381204 * A245690 A146291 A327538

Adjacent sequences: A382965 A382966 A382967 * A382969 A382970 A382971

Keyword

nonn,easy

Author

Amiram Eldar, Apr 10 2025

Status

approved