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 A382421 #7 Mar 25 2025 10:11:45
%S A382421 3,4,3,3,5,3,4,3,3,6,6,4,4,3,5,3,6,4,3,3,7,3,3,8,3,5,4,3,4,3,3,6,6,4,
%T A382421 9,5,3,4,5,3,3,8,3,3,4,3,10,3,3,4,3,6,8,3,4,3,3,3,5,6,4,3,3,3,7,6,8,4,
%U A382421 3,5,3,12,3,6,3,3,4,3,5,5,3,4,6,6,9,3,3
%N A382421 The product of exponents in the prime factorization of the noncubefree numbers.
%H A382421 Amiram Eldar, <a href="/A382421/b382421.txt">Table of n, a(n) for n = 1..10000</a>
%F A382421 a(n) = A005361(A046099(n)).
%F A382421 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = (zeta(2)*zeta(3)^2/zeta(6) - zeta(3) * Product_{p prime} (1 + 1/p^2 - 2/p^3))/(zeta(3) - 1) = (A082695 - A330594) * A002117 / (A002117 - 1) = 4.97723390794900554553... .
%t A382421 s[n_] := Times @@ FactorInteger[n][[;; , 2]]; noncubeFreeQ[n_] := Max[FactorInteger[n][[;; , 2]]] > 2; s /@ Select[Range[600], noncubeFreeQ]
%o A382421 (PARI) list(kmax) = {my(e); for(k = 2, kmax, e = factor(k)[, 2]; if(vecmax(e) > 2, print1(vecprod(e), ", "))); }
%Y A382421 Cf. A002117, A013661, A013664, A005361, A046099, A082695, A330594, A368039, A382419.
%K A382421 nonn,easy
%O A382421 1,1
%A A382421 _Amiram Eldar_, Mar 25 2025