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 A382969 #11 Apr 14 2025 06:18:10
%S A382969 2,3,2,2,4,2,3,2,2,5,3,3,3,2,4,2,3,3,2,2,6,2,2,4,2,4,3,2,3,2,2,5,3,3,
%T A382969 4,4,2,3,4,2,2,7,2,2,3,2,5,2,2,3,2,5,4,2,3,2,2,2,4,3,3,2,2,2,6,3,4,3,
%U A382969 2,4,2,5,2,5,2,2,3,2,4,4,2,3,3,3,8,2,2
%N A382969 The excess of the n-th noncubefree number.
%H A382969 Amiram Eldar, <a href="/A382969/b382969.txt">Table of n, a(n) for n = 1..10000</a>
%F A382969 a(n) = A046660(A046099(n)).
%F A382969 a(n) >= 2.
%F A382969 Asymptotic mean: lim_{m->oo} (1/m) Sum_{k=1..m} a(k) = ((Sum_{p prime} 1/(p*(p-1))) - (1/zeta(3)) * (Sum_{p prime} (p-1)/(p^3-1))) / (1-1/zeta(3)) = 3.12223294188308957729... .
%e A382969 a(1) = 2 since the 1st noncubefree number is A046099(1) = 8 = 2^3. It has 3 prime factors when counted with multiplicity, and 1 distinct prime factor, so a(1) = 3 - 1 = 2.
%t A382969 f[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, If[Max[e] < 3, Nothing, Total[e] - Length[e]]]; Array[f, 100]
%o A382969 (PARI) list(lim) = {my(e); for(k = 2, lim, e = factor(k)[,2]; if(vecmax(e) > 2, print1(vecsum(e) - #e, ", ")));}
%Y A382969 Cf. A002117, A046099, A046660, A136141, A275699, A376366.
%K A382969 nonn,easy
%O A382969 1,1
%A A382969 _Amiram Eldar_, Apr 10 2025