A304687 Start with the multiset of prime multiplicities of n. Given a multiset, take the multiset of its multiplicities. Repeat until a constant multiset {k,k,...,k} is reached, and set a(n) to the sum of this multiset (k times the length).

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 2, 4, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 3, 2, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 2, 1, 3, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 6, 2, 3, 1, 2, 2, 3, 1, 2, 1, 2, 2, 2, 2, 3, 1, 2, 4, 2, 1, 2, 2, 2, 2

Offset: 1

Author

Gus Wiseman, May 16 2018

Keywords

• nonn

Examples

			The following are examples showing the reduction of a multiset starting with the multiset of prime multiplicities of n.
         a(60) = 2: {1,1,2} -> {1,2} -> {1,1}.
        a(360) = 3: {1,2,3} -> {1,1,1}.
       a(1260) = 4: {1,1,2,2} -> {2,2}.
a(21492921450) = 6: {1,1,2,2,3,3} -> {2,2,2}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A001221, A001222, A071625, A112798, A181819, A182850, A182857, A304465, A304634, A304636.

Programs

Maple

a:= proc(n) map(i-> i[2], ifactors(n)[2]);
      while nops({%[]})>1 do [coeffs(add(x^i, i=%))] od;
      add(i, i=%)
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, May 17 2018

Mathematica

Table[If[n==1,0,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],!SameQ@@#&]//Total],{n,360}]