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 A323014 #13 Jun 12 2022 15:39:38 %S A323014 0,1,1,2,1,3,1,2,2,3,1,4,1,3,3,2,1,4,1,4,3,3,1,4,2,3,2,4,1,3,1,2,3,3, %T A323014 3,3,1,3,3,4,1,3,1,4,4,3,1,4,2,4,3,4,1,4,3,4,3,3,1,5,1,3,4,2,3,3,1,4, %U A323014 3,3,1,4,1,3,4,4,3,3,1,4,2,3,1,5,3,3,3,4,1,5,3,4,3,3,3,4,1,4,4,3,1,3,1,4,3 %N A323014 a(1) = 0; a(prime) = 1; otherwise a(n) = 1 + a(A181819(n)). %C A323014 Except for n = 2, same as A182850. Unlike A182850, the terms of this sequence depend only on the prime signature (A101296, A118914) of the index. %H A323014 Antti Karttunen, <a href="/A323014/b323014.txt">Table of n, a(n) for n = 1..100000</a> %H A323014 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a> %F A323014 For all n >= 1, a(n) = a(A046523(n)). [See comment] - _Antti Karttunen_, Jun 10 2022 %t A323014 dep[n_]:=If[n==1,0,If[PrimeQ[n],1,1+dep[Times@@Prime/@Last/@FactorInteger[n]]]]; %t A323014 Array[dep,100] %o A323014 (PARI) %o A323014 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2]))); %o A323014 A323014(n) = if(1==n,0,if(isprime(n),1, 1+A323014(A181819(n)))); \\ _Antti Karttunen_, Jun 10 2022 %Y A323014 Positions of 1's are the prime numbers A000040. %Y A323014 Positions of 2's are the proper prime powers A246547. %Y A323014 Positions of 3's are A182853. %Y A323014 Row lengths of A323023. %Y A323014 Cf. A001221, A001222, A046523, A056239, A070175, A071625, A101296, A112798, A118914, A181819, A181821, A182850, A182857, A304465, A323022. %K A323014 nonn %O A323014 1,4 %A A323014 _Gus Wiseman_, Jan 02 2019 %E A323014 Terms a(88) and beyond from _Antti Karttunen_, Jun 10 2022