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A326647 Number of factorizations of n into factors > 1 with integer average and integer geometric mean. 14
0, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 3, 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, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
LINKS
Wikipedia, Geometric mean
EXAMPLE
The a(216) = 5 factorizations:
(2*4*27)
(3*3*24)
(3*6*12)
(6*6*6)
(216)
The a(729) = 8 factorizations:
(3*3*3*3*3*3)
(3*3*81)
(3*9*27)
(3*243)
(9*9*9)
(9*81)
(27*27)
(729)
MATHEMATICA
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], IntegerQ[Mean[#]]&&IntegerQ[GeometricMean[#]]&]], {n, 2, 100}]
CROSSREFS
Positions of terms > 1 are the perfect powers A001597.
Factorizations with integer average are A326622.
Factorizations with integer geometric mean are A326028.
Partitions with integer average and geometric mean are A326641.
Sequence in context: A305253 A294336 A316782 * A326028 A294338 A316790
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 16 2019
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)