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A325759 Number of distinct frequencies in the frequency span of n. 3
0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 3, 2, 1, 2, 1, 3, 3, 3, 1, 3, 2, 3, 2, 3, 1, 3, 1, 2, 3, 3, 4, 2, 1, 3, 3, 3, 1, 4, 1, 3, 3, 3, 1, 3, 2, 3, 3, 3, 1, 3, 4, 4, 3, 3, 1, 3, 1, 3, 3, 2, 4, 4, 1, 3, 3, 3, 1, 3, 1, 3, 3, 3, 4, 4, 1, 4, 2, 3, 1, 3, 4, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

We define the frequency span of an integer partition to be the partition itself if it has no or only one block, and otherwise it is the multiset union of the partition and the frequency span of its multiplicities. For example, the frequency span of (3,2,2,1) is {1,2,2,3} U {1,1,2} U {1,2} U {1,1} U {2} = {1,1,1,1,1,1,2,2,2,2,2,3}. The frequency span of a positive integer n is the frequency span of its prime indices (row n of A296150).

LINKS

Table of n, a(n) for n=1..87.

MATHEMATICA

primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];

freqspan[ptn_]:=If[Length[ptn]<=1, ptn, Sort[Join[ptn, freqspan[Sort[Length/@Split[ptn]]]]]];

Table[Length[Union[freqspan[primeMS[n]]]], {n, 100}]

CROSSREFS

Row lengths of A325758.

Number of distinct entries in row n of A325757.

Cf. A001221, A001222, A056239, A071625, A112798, A181819, A182857, A323014, A325249, A325277, A325760.

Sequence in context: A327925 A320012 A241276 * A292286 A341596 A099042

Adjacent sequences:  A325756 A325757 A325758 * A325760 A325761 A325762

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 19 2019

STATUS

approved

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Last modified September 19 08:05 EDT 2021. Contains 347556 sequences. (Running on oeis4.)