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 A343222 #12 May 23 2021 03:20:54
%S A343222 0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,2,0,1,0,1,0,0,0,2,0,0,0,1,0,1,0,2,0,0,
%T A343222 0,2,0,0,0,2,0,0,0,1,0,0,0,2,0,0,0,1,0,1,0,2,0,0,0,2,0,0,0,3,0,0,0,1,
%U A343222 0,0,0,2,0,0,0,1,0,0,0,2,1,0,0,1,0,0,0,2,0,1,0,1,0,0,0,3,0,0,0,1,0,0,0,2,0
%N A343222 Number of iterations of x -> A003961(x) needed until A003415(x) <= x, when starting from x=n, where A003415(x) gives the arithmetic derivative of x, and A003961 shifts its prime factorization one step towards the larger primes.
%H A343222 Antti Karttunen, <a href="/A343222/b343222.txt">Table of n, a(n) for n = 1..65537</a>
%o A343222 (PARI)
%o A343222 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A343222 A003961(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
%o A343222 A343222(n) = if(A003415(n)<=n,0,1+A343222(A003961(n)));
%Y A343222 Cf. A003415, A003961.
%Y A343222 Positions of zeros: Union of A051674 and A083347.
%Y A343222 Cf. also A343221, A344027.
%K A343222 nonn
%O A343222 1,16
%A A343222 _Antti Karttunen_, Apr 08 2021