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A340828
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Number of strict integer partitions of n whose maximum part is a multiple of their length.
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12
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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
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OFFSET
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1,3
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Divisible[Max@@#, Length[#]]&]], {n, 30}]
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CROSSREFS
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Note: A-numbers of Heinz-number sequences are in parentheses below.
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.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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