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A340828 Number of strict integer partitions of n whose maximum part is a multiple of their length. 12
1, 1, 2, 1, 2, 3, 3, 2, 4, 5, 6, 6, 7, 8, 11, 10, 13, 17, 18, 21, 24, 27, 30, 35, 39, 46, 53, 61, 68, 79, 87, 97, 110, 123, 139, 157, 175, 196, 222, 247, 278, 312, 347, 385, 433, 476, 531, 586, 651, 720, 800, 883, 979, 1085, 1200, 1325, 1464, 1614, 1777 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
EXAMPLE
The a(1) = 1 through a(16) = 10 partitions (A..G = 10..16):
1 2 3 4 5 6 7 8 9 A B C D E F G
21 41 42 43 62 63 64 65 84 85 86 87 A6
321 61 81 82 83 A2 A3 A4 A5 C4
621 631 A1 642 C1 C2 C3 E2
4321 632 651 643 653 E1 943
641 921 652 932 654 952
931 941 942 961
8321 951 C31
C21 8431
8421 8521
54321
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[Max@@#, Length[#]]&]], {n, 30}]
CROSSREFS
Note: A-numbers of Heinz-number sequences are in parentheses below.
The non-strict version is A168659 (A340609/A340610).
A018818 counts partitions into divisors (A326841).
A047993 counts balanced partitions (A106529).
A064173 counts partitions of positive/negative rank (A340787/A340788).
A067538 counts partitions whose length/max divides sum (A316413/A326836).
A072233 counts partitions by sum and length, with strict case A008289.
A096401 counts strict partition with length equal to minimum.
A102627 counts strict partitions with length dividing sum.
A326842 counts partitions whose length and parts all divide sum (A326847).
A326850 counts strict partitions whose maximum part divides sum.
A326851 counts strict partitions with length and maximum dividing sum.
A340829 counts strict partitions with Heinz number divisible by sum.
A340830 counts strict partitions with all parts divisible by length.
Sequence in context: A024376 A230128 A342095 * A123265 A104345 A244516
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 01 2021
STATUS
approved

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Last modified February 28 19:33 EST 2024. Contains 370400 sequences. (Running on oeis4.)