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 A078374 Number of partitions of n into distinct and relatively prime parts. 68
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..10000 N. J. A. Sloane, Transforms FORMULA 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 EXAMPLE 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) MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&GCD@@#==1&]], {n, 15}] (* Gus Wiseman, Oct 18 2020 *) CROSSREFS 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 KEYWORD nonn AUTHOR Vladeta Jovovic, Dec 24 2002 STATUS approved

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Last modified May 16 21:28 EDT 2021. Contains 343951 sequences. (Running on oeis4.)