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A078374
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Number of partitions of n into distinct and relatively prime parts.
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68
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1, 0, 1, 1, 2, 2, 4, 4, 6, 7, 11, 10, 17, 17, 23, 26, 37, 36, 53, 53, 70, 77, 103, 103, 139, 147, 184, 199, 255, 260, 339, 358, 435, 474, 578, 611, 759, 810, 963, 1045, 1259, 1331, 1609, 1726, 2015, 2200, 2589, 2762, 3259, 3509, 4058, 4416, 5119, 5488, 6364, 6882
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OFFSET
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1,5
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COMMENTS
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The Heinz numbers of these partitions are given by A302796, which is the intersection of A005117 (strict) and A289509 (relatively prime). - Gus Wiseman, Oct 18 2020
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 1..10000
N. J. A. Sloane, Transforms
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FORMULA
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Moebius transform of A000009.
G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n). - Ilya Gutkovskiy, Apr 26 2017
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EXAMPLE
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From Gus Wiseman, Oct 18 2020: (Start)
The a(1) = 1 through a(13) = 17 partitions (empty column indicated by dot, A = 10, B = 11, C = 12):
1 . 21 31 32 51 43 53 54 73 65 75 76
41 321 52 71 72 91 74 B1 85
61 431 81 532 83 543 94
421 521 432 541 92 651 A3
531 631 A1 732 B2
621 721 542 741 C1
4321 632 831 643
641 921 652
731 5421 742
821 6321 751
5321 832
841
931
A21
5431
6421
7321
(End)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&GCD@@#==1&]], {n, 15}] (* Gus Wiseman, Oct 18 2020 *)
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CROSSREFS
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Cf. A047966.
A000837 is the not necessarily strict version.
A302796 gives the Heinz numbers of these partitions.
A305713 is the pairwise coprime instead of relatively prime version.
A332004 is the ordered version.
A337452 is the case without 1's.
A000009 counts strict partitions.
A000740 counts relatively prime compositions.
Cf. A007359, A101268, A289508, A289509, A291166, A298748, A337451, A337485, A337451, A337561, A337563.
Sequence in context: A122134 A035940 A067772 * A341697 A242984 A027590
Adjacent sequences: A078371 A078372 A078373 * A078375 A078376 A078377
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic, Dec 24 2002
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STATUS
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approved
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