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A339619
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Number of integer partitions of n with no 1's and a part divisible by all the other parts.
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8
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1, 0, 1, 1, 2, 1, 4, 1, 5, 3, 7, 2, 13, 2, 13, 9, 17, 6, 27, 7, 33, 19, 35, 16, 58, 22, 58, 39, 75, 37, 108, 44, 117, 75, 132, 88, 190, 94, 199, 147, 250, 153, 322, 180, 363, 271, 405, 286, 544, 339, 601, 458, 699, 503, 868, 608, 990, 777, 1113, 865, 1422, 993
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OFFSET
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0,5
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COMMENTS
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Alternative name: Number of integer partitions of n with no 1's that are empty or have greatest part divisible by all the other parts.
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LINKS
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EXAMPLE
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The a(6) = 4 through a(16) = 17 partitions (A..G = 10..16):
6 7 8 9 A B C D E F G
33 44 63 55 632 66 6322 77 A5 88
42 62 333 82 84 C2 C3 C4
222 422 442 93 662 555 E2
2222 622 A2 842 663 844
4222 444 A22 933 C22
22222 633 4442 6333 4444
822 6332 33333 6622
3333 8222 63222 8422
4422 44222 A222
6222 62222 44422
42222 422222 63322
222222 2222222 82222
442222
622222
4222222
22222222
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MATHEMATICA
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Table[If[n==0, 1, Length[Select[IntegerPartitions[n], FreeQ[#, 1]&&Or@@And@@IntegerQ/@(Max@@#/#)&]]], {n, 0, 30}]
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CROSSREFS
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The version with 1's allowed is A130689.
The Heinz numbers of these partitions are the odd complement of A343337.
The strict case with 1's allowed is A343347.
A000070 counts partitions with a selected part.
A006128 counts partitions with a selected position.
A015723 counts strict partitions with a selected part.
Cf. A066186, A083710, A083711, A097986, A130714, A338470, A343341, A343342, A343346, A343377, A343382.
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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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