# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a304455 Showing 1-1 of 1 %I A304455 #17 Dec 06 2018 16:33:30 %S A304455 0,0,0,1,0,2,0,1,1,2,0,3,0,2,2,1,0,3,0,3,2,2,0,3,1,2,1,3,0,2,0,1,2,2, %T A304455 2,2,0,2,2,3,0,2,0,3,3,2,0,3,1,3,2,3,0,3,2,3,2,2,0,4,0,2,3,1,2,2,0,3, %U A304455 2,2,0,3,0,2,3,3,2,2,0,3,1,2,0,4,2,2,2,3,0,4,2,3,2,2,2,3,0,3,3,2,0,2,0,3,2 %N A304455 Number of steps in the reduction to a multiset of size 1 of the multiset of prime factors of n, obtained by repeatedly taking the multiset of multiplicities. %H A304455 Antti Karttunen, Table of n, a(n) for n = 1..20000 %H A304455 Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000 %H A304455 Index entries for sequences computed from exponents in factorization of n %F A304455 For n > 2, a(n) = A182850(n) - 1. %F A304455 a(prime(n)) = 0. %F A304455 a(A246547(n)) = 1. %e A304455 The a(2520) = 5 steps are {2,2,2,3,3,5,7} -> {1,1,2,3} -> {1,1,2} -> {1,2} -> {1,1} -> {2}. %t A304455 Table[Length[Select[FixedPointList[Sort[Length/@Split[#]]&,If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[p,{k}]]]]],Length[#]>1&]],{n,100}] %o A304455 (PARI) %o A304455 A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2]))); %o A304455 A304455(n) = if(n<=2,0, n=A181819(n); if(2==n,0,1+A304455(n))); \\ _Antti Karttunen_, Dec 06 2018 %Y A304455 Cf. A000961, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A130091, A181819, A182850, A182853, A182857, A303945, A304464, A304465, A320118. %K A304455 nonn %O A304455 1,6 %A A304455 _Gus Wiseman_, May 12 2018 %E A304455 More terms from _Antti Karttunen_, Dec 06 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE