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A370803
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Number of integer partitions of n such that more than one set can be obtained by choosing a different divisor of each part.
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19
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0, 0, 1, 1, 1, 3, 2, 4, 5, 7, 10, 11, 15, 18, 25, 28, 39, 45, 59, 66, 83, 101, 123, 150, 176, 213, 252, 301, 352, 426, 497, 589, 684, 802, 939, 1095, 1270
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OFFSET
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0,6
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LINKS
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EXAMPLE
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The partition (6,4,4,1) has two choices, namely {1,2,4,6} and {1,2,3,4}, so is counted under a(15).
The a(0) = 0 through a(13) = 18 partitions (A..D = 10..13):
. . 2 3 4 5 6 7 8 9 A B C D
32 42 43 44 54 64 65 66 76
41 52 53 63 73 74 75 85
61 62 72 82 83 84 94
431 81 91 92 93 A3
432 433 A1 A2 B2
621 532 443 543 C1
541 542 633 544
622 632 642 643
631 641 651 652
821 732 661
741 742
822 832
831 841
921 922
A21
5431
6421
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[Union[Sort /@ Select[Tuples[Divisors/@#], UnsameQ@@#&]]]>1&]], {n, 0, 30}]
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CROSSREFS
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Including partitions with one choice gives A239312, complement A370320.
These partitions have ranks A370811.
A355731 counts choices of a divisor of each prime index, firsts A355732.
A355733 counts divisor-choices of prime indices.
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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