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A326515 Number of factorizations of n into factors > 1 where every factor has the same average of prime indices. 18
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
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
Sequence in context: A070012 A071178 A366895 * A319864 A072776 A077481
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2019
STATUS
approved

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Last modified April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)