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.

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, 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, 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

Offset: 1

Author

Gus Wiseman, May 12 2018

Keywords

• nonn

Examples

			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}.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000
• Index entries for sequences computed from exponents in factorization of n

Crossrefs

Cf. A000961, A001222, A001597, A005117, A007916, A055932, A056239, A112798, A130091, A181819, A182850, A182853, A182857, A303945, A304464, A304465, A320118.

Programs

Mathematica

Table[Length[Select[FixedPointList[Sort[Length/@Split[#]]&,If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[p,{k}]]]]],Length[#]>1&]],{n,100}]

PARI

A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
A304455(n) = if(n<=2,0, n=A181819(n); if(2==n,0,1+A304455(n))); \\ Antti Karttunen, Dec 06 2018

Formula

For n > 2, a(n) = A182850(n) - 1.

a(prime(n)) = 0.

a(A246547(n)) = 1.

Extensions

More terms from Antti Karttunen, Dec 06 2018