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 A328311 #10 Oct 13 2019 18:09:30 %S A328311 0,0,0,1,0,1,0,0,0,1,0,3,0,2,3,2,0,0,0,2,1,1,0,0,0,1,1,4,0,1,0,0,1,1, %T A328311 2,1,0,1,4,0,0,1,0,3,0,2,0,1,0,1,2,2,0,2,4,0,1,1,0,1,0,1,0,1,2,1,0,2, %U A328311 1,1,0,0,0,1,0,3,2,1,0,1,0,1,0,1,1,2,5,0,0,0,2,4,1,2,3,0,0,0,1,1,0,1,0,0,1 %N A328311 a(n) = 1 + A051903(A003415(n)) - A051903(n), a(1) = 0 by convention. %C A328311 All terms are nonnegative because taking the arithmetic derivative (A003415) of n may decrease its "degree" (i.e., its maximal exponent, A051903) by at most one, and in many cases may also increase it, or keep it same. %H A328311 Antti Karttunen, <a href="/A328311/b328311.txt">Table of n, a(n) for n = 1..65537</a> %F A328311 a(1) = 0, for n > 1, a(n) = 1 + A051903(A003415(n)) - A051903(n). %F A328311 For n > 1, a(n) = 1 + A328310(n). %o A328311 (PARI) %o A328311 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1])); %o A328311 A051903(n) = if((1==n),0,vecmax(factor(n)[, 2])); %o A328311 A328311(n) = if(n<=1,0,1+(A051903(A003415(n)) - A051903(n))); %Y A328311 One more than A328310. %Y A328311 Cf. A003415, A051903, A328312. %Y A328311 Cf. A328320 (indices of zeros), A328321 (of nonzero terms). %K A328311 nonn %O A328311 1,12 %A A328311 _Antti Karttunen_, Oct 13 2019