This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382966 #7 Apr 11 2025 08:46:32
%S A382966 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,
%T A382966 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,
%U A382966 1,2,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,2,1
%N A382966 The number of non-unitary prime divisors of the n-th biquadratefree number that is not cubefree.
%H A382966 Amiram Eldar, <a href="/A382966/b382966.txt">Table of n, a(n) for n = 1..10000</a>
%F A382966 a(n) = A056170(A375072(n)).
%F A382966 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... .
%t A382966 f[k_] := If[k == 1, Nothing, Module[{e = FactorInteger[k][[;; , 2]]}, If[Max[e] == 3, Count[e, _?(# > 1 &)], Nothing]]]; Array[f, 1000]
%o A382966 (PARI) list(lim) = {my(e); for(k = 2, lim, e = factor(k)[, 2]; if(vecmax(e) == 3, print1(#select(x -> x > 1, e), ", ")));}
%Y A382966 Cf. A002117, A013662, A056170, A375072, A376366, A382425, A382965, A382968.
%K A382966 nonn,easy
%O A382966 1,7
%A A382966 _Amiram Eldar_, Apr 10 2025