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 A375667 #7 Aug 23 2024 10:43:06
%S A375667 0,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A375667 1,1,1,1,1,1,2,3,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,
%U A375667 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,1,1,1,1,1,1,1,1
%N A375667 The maximum exponent in the prime factorization of the 5-rough numbers (A007310).
%H A375667 Amiram Eldar, <a href="/A375667/b375667.txt">Table of n, a(n) for n = 1..10000</a>
%F A375667 a(n) = A051903(A007310(n)).
%F A375667 Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1 + Sum_{k>=2} (1 - 1/((1-1/2^k) * (1-1/3^k) * zeta(k))) = 1.1034178389191320571029... .
%t A375667 a[n_] := Max[FactorInteger[6*Floor[n/2] - (-1)^n][[;; , 2]]]; a[1] = 0; Array[a, 100]
%o A375667 (PARI) a(n) = if(n == 1, 0, vecmax(factor(n\2*6-(-1)^n)[,2]));
%Y A375667 Cf. A007310, A051903, A375039, A375668.
%K A375667 nonn,easy
%O A375667 1,9
%A A375667 _Amiram Eldar_, Aug 23 2024