|
|
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
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|