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 A328391 #9 Oct 15 2019 17:21:51 %S A328391 0,0,1,1,1,0,1,3,1,1,1,1,2,1,1,4,1,2,2,2,2,2,2,3,3,3,3,3,3,0,2,1,1,1, %T A328391 1,2,1,1,1,1,1,1,1,2,2,1,1,2,2,2,2,2,2,3,3,3,3,3,3,1,1,1,1,2,1,1,1,1, %U A328391 1,2,1,3,1,1,1,1,1,2,2,7,2,2,2,3,3,3,3,3,3,2,2,4,2,2,2,2,2,2,2,3,2,2,2,2,2 %N A328391 Maximal exponent in the prime factorization of A327860(n): a(n) = A051903(A327860(n)). %H A328391 Antti Karttunen, <a href="/A328391/b328391.txt">Table of n, a(n) for n = 1..30030</a> %H A328391 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a> %F A328391 a(n) = A051903(A327860(n)) = A051903(A003415(A276086(n))). %F A328391 a(A002110(n)) = 0 for all n >= 0. %F A328391 For all n >= 1, a(n) >= A328114(n)-1. [Because arithmetic derivative will decrease the maximal prime exponent (A051903) of its argument by at most one] %o A328391 (PARI) %o A328391 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2])); %o A328391 A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); }; %o A328391 A328391(n) = A051903(A327860(n)); %Y A328391 Cf. A002110, A003415, A051903, A276086, A327860, A327969, A328114, A328388, A328389, A328390, A328392. %K A328391 nonn %O A328391 1,8 %A A328391 _Antti Karttunen_, Oct 15 2019