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%I #20 Oct 22 2020 06:49:41
%S 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,
%T 147,184,199,255,260,339,358,435,474,578,611,759,810,963,1045,1259,
%U 1331,1609,1726,2015,2200,2589,2762,3259,3509,4058,4416,5119,5488,6364,6882
%N Number of partitions of n into distinct and relatively prime parts.
%C 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
%H Seiichi Manyama, <a href="/A078374/b078374.txt">Table of n, a(n) for n = 1..10000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F Moebius transform of A000009.
%F G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n). - _Ilya Gutkovskiy_, Apr 26 2017
%e From _Gus Wiseman_, Oct 18 2020: (Start)
%e The a(1) = 1 through a(13) = 17 partitions (empty column indicated by dot, A = 10, B = 11, C = 12):
%e 1 . 21 31 32 51 43 53 54 73 65 75 76
%e 41 321 52 71 72 91 74 B1 85
%e 61 431 81 532 83 543 94
%e 421 521 432 541 92 651 A3
%e 531 631 A1 732 B2
%e 621 721 542 741 C1
%e 4321 632 831 643
%e 641 921 652
%e 731 5421 742
%e 821 6321 751
%e 5321 832
%e 841
%e 931
%e A21
%e 5431
%e 6421
%e 7321
%e (End)
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&GCD@@#==1&]],{n,15}] (* _Gus Wiseman_, Oct 18 2020 *)
%Y Cf. A047966.
%Y A000837 is the not necessarily strict version.
%Y A302796 gives the Heinz numbers of these partitions.
%Y A305713 is the pairwise coprime instead of relatively prime version.
%Y A332004 is the ordered version.
%Y A337452 is the case without 1's.
%Y A000009 counts strict partitions.
%Y A000740 counts relatively prime compositions.
%Y Cf. A007359, A101268, A289508, A289509, A291166, A298748, A337451, A337485, A337451, A337561, A337563.
%K nonn
%O 1,5
%A _Vladeta Jovovic_, Dec 24 2002
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