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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). 8
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 (list; graph; refs; listen; history; text; internal format)
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: A077480 A059829 A304465 * A076558 A235875 A204893

Adjacent sequences:  A304684 A304685 A304686 * A304688 A304689 A304690

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 16 2018

STATUS

approved

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Last modified April 18 22:08 EDT 2019. Contains 322237 sequences. (Running on oeis4.)