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A326515 Number of factorizations of n into factors > 1 where every factor has the same average of prime indices. 15
1, 1, 1, 2, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 7, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 2, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

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

Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

EXAMPLE

The a(900) = 9 factorizations:

  (3*3*10*10),

  (3*3*100), (3*10*30), (9*10*10),

  (3*300), (9*100), (10*90), (30*30),

  (900).

MATHEMATICA

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

facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]];

Table[Length[Select[facs[n], SameQ@@Mean/@primeMS/@#&]], {n, 100}]

CROSSREFS

Cf. A001055, A038041, A051293, A321455, A321469, A322794, A326512, A326514, A326516, A326520, A326536.

Sequence in context: A051904 A070012 A071178 * A319864 A072776 A077481

Adjacent sequences:  A326512 A326513 A326514 * A326516 A326517 A326518

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 12 2019

STATUS

approved

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Last modified February 23 13:33 EST 2020. Contains 332159 sequences. (Running on oeis4.)