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A328675
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Number of integer partitions of n with no two distinct consecutive parts divisible.
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2
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1, 1, 2, 2, 3, 3, 4, 5, 6, 8, 9, 13, 13, 22, 23, 30, 36, 50, 54, 77, 85, 113, 135, 170, 194, 256, 303, 369, 440, 545, 640, 792, 931, 1132, 1347, 1616, 1909, 2295, 2712, 3225, 3799, 4519, 5310, 6278, 7365, 8675, 10170, 11928, 13940, 16314, 19046, 22223, 25856
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OFFSET
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0,3
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LINKS
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EXAMPLE
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The a(1) = 1 through a(10) = 9 partitions (A = 10).
1 2 3 4 5 6 7 8 9 A
11 111 22 32 33 43 44 54 55
1111 11111 222 52 53 72 64
111111 322 332 333 73
1111111 2222 432 433
11111111 522 532
3222 3322
111111111 22222
1111111111
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], !MatchQ[Union[#], {___, x_, y_, ___}/; Divisible[y, x]]&]], {n, 0, 30}]
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CROSSREFS
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The Heinz numbers of these partitions are given by A328674.
The case involving all consecutive parts (not just distinct) is A328171.
The version for relative primality instead of divisibility is A328187.
Partitions with all consecutive parts divisible are A003238.
Compositions without consecutive divisibilities are A328460.
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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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