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

1,4

Links

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

Example

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}.

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}]

Crossrefs

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

Sequence in context: A059829 A363369 A304465 * A076558 A328195 A235875

Adjacent sequences: A304684 A304685 A304686 * A304688 A304689 A304690

Keyword

nonn

Author

Gus Wiseman, May 16 2018

Status

approved