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A316440 Number of integer partitions of n such that every submultiset has an integer average. 5
1, 1, 2, 2, 4, 2, 6, 2, 7, 5, 8, 2, 13, 2, 10, 10, 14, 2, 20, 2, 17, 15, 14, 2, 32, 3, 16, 22, 25, 2, 40, 2, 27, 30, 20, 4, 58, 2, 22, 40, 40, 2, 64, 2, 40, 53, 26, 2, 93, 3, 30, 64, 54, 2, 94, 4, 58, 78, 32, 2, 138, 2, 34, 96, 75, 10, 131, 2, 76, 111, 48, 2, 192, 2, 40, 138, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
For a prime p, a(p) = 2. - Max Alekseyev, Sep 02 2023
EXAMPLE
The a(12) = 13 partitions:
(12),
(6,6), (7,5), (8,4), (9,3), (10,2), (11,1),
(4,4,4), (6,4,2), (8,2,2),
(3,3,3,3),
(2,2,2,2,2,2),
(1,1,1,1,1,1,1,1,1,1,1,1).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], And@@IntegerQ/@Mean/@Union[Rest[Subsets[#]]]&]], {n, 20}]
CROSSREFS
Sequence in context: A360593 A080221 A137849 * A118982 A129457 A275365
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 03 2018
EXTENSIONS
a(0) prepended and more terms added by Max Alekseyev, Sep 02 2023
STATUS
approved

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Last modified June 20 17:22 EDT 2024. Contains 373530 sequences. (Running on oeis4.)