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A328966 Number of strict factorizations of n with integer average. 23
1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 2, 2, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 2, 3, 1, 1, 5, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 5, 1, 1, 3, 3, 2, 1, 1, 2, 2, 1, 1, 5, 1, 1, 3, 2, 2, 2, 1, 5, 2, 1, 1, 4, 2, 1, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,7
LINKS
EXAMPLE
The a(n) factorizations for n = 2, 8, 24, 48, 96:
(2) (8) (24) (32) (48) (96)
(2*4) (4*6) (4*8) (6*8) (2*48)
(2*12) (2*16) (2*24) (4*24)
(2*3*4) (4*12) (6*16)
(2*4*6) (8*12)
(3*4*8)
(2*3*16)
(2*4*12)
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], UnsameQ@@#&&IntegerQ[Mean[#]]&]], {n, 2, 100}]
CROSSREFS
The non-strict version is A326622.
Partitions with integer average are A067538.
Strict partitions with integer average are A102627.
Heinz numbers of partitions with integer average are A316413.
Factorizations with integer geometric mean are A326028.
Sequence in context: A072273 A157230 A034380 * A077479 A335225 A070106
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 16 2019
STATUS
approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)