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 A375668 #6 Aug 23 2024 10:43:15
%S A375668 0,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,
%T A375668 1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A375668 1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,2,1,1,1,1,1,1,1,1
%N A375668 The maximum exponent in the prime factorization of the 7-rough numbers (A007775).
%H A375668 Amiram Eldar, <a href="/A375668/b375668.txt">Table of n, a(n) for n = 1..10000</a>
%F A375668 a(n) = A051903(A007775(n)).
%F A375668 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) * (1-1/5^k) * zeta(k))) = 1.05546104674564363968... .
%F A375668 In general, the asymptotic mean of the maximum exponent in the prime factorization of the p-rough numbers (numbers that are not divisible by any prime smaller than p) is 1 + Sum_{k>=2} (1 - 1/(zeta(k) * Product_{primes q < p} (1-1/q^k))).
%t A375668 If[# == 1, 0, Max[FactorInteger[#][[;; , 2]]]] & /@ Select[Range[300], CoprimeQ[#, 30] &]
%o A375668 (PARI) lista(nmax) = print1(0, ", "); for(n = 2, nmax, if(gcd(n, 30) == 1, print1(vecmax(factor(n)[,2]), ", ")));
%Y A375668 Cf. A007775, A051903, A375039, A375667.
%K A375668 nonn,easy
%O A375668 1,14
%A A375668 _Amiram Eldar_, Aug 23 2024