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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 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: A070012 A071178 A366895 * 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 April 25 10:51 EDT 2024. Contains 371967 sequences. (Running on oeis4.)