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 A337563 Number of pairwise coprime unordered triples of positive integers > 1 summing to n. 19
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 1, 4, 0, 7, 1, 7, 3, 9, 2, 15, 3, 13, 5, 17, 4, 29, 5, 20, 8, 28, 8, 42, 8, 31, 14, 42, 10, 59, 12, 45, 21, 52, 14, 77, 17, 68, 26, 69, 19, 101, 26, 84, 34, 86, 25, 138, 28, 95, 43, 111, 36, 161, 35, 118, 52, 151 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,13 COMMENTS Such partitions are necessarily strict. The Heinz numbers of these partitions are the intersection of A005408 (no 1's), A014612 (triples), and A302696 (coprime). LINKS Fausto A. C. Cariboni, Table of n, a(n) for n = 0..10000 EXAMPLE The a(10) = 1 through a(24) = 15 triples (empty columns indicated by dots, A..J = 10..19):   532  .  543  .  743  753  754  .  765  B53  875  975  985  B75  987           732     752       853     873       974  B73  B65  D73  B76                             952     954       A73  D53  B74       B85                             B32     972       B54       B83       B94                                     B43       B72       B92       BA3                                     B52       D43       D54       C75                                     D32       D52       D72       D65                                                         E53       D74                                                         H32       D83                                                                   D92                                                                   F72                                                                   G53                                                                   H43                                                                   H52                                                                   J32 MATHEMATICA Table[Length[Select[IntegerPartitions[n, {3}], !MemberQ[#, 1]&&CoprimeQ@@#&]], {n, 0, 30}] CROSSREFS A055684 is the version for pairs. A220377 allows 1's, with non-strict version A307719. A337485 counts these partitions of any length. A337563*6 is the ordered version. A001399(n - 3) = A069905(n) = A211540(n + 2) counts 3-part partitions. A002865 counts partitions with no 1's, with strict case A025147. A007359 counts pairwise coprime partitions with no 1's. A078374 counts relatively prime strict partitions. A200976 and A328673 count pairwise non-coprime partitions. A302696 ranks pairwise coprime partitions. A302698 counts relatively prime partitions with no 1's. A305713 counts pairwise coprime strict partitions. A327516 counts pairwise coprime partitions. A337452 counts relatively prime strict partitions with no 1's. Cf. A007304, A082024, A101268, A284825, A332004, A337451, A337461, A337462, A337561, A337599, A337601, A337605. Sequence in context: A053470 A308202 A329152 * A278648 A029181 A261426 Adjacent sequences:  A337560 A337561 A337562 * A337564 A337565 A337566 KEYWORD nonn AUTHOR Gus Wiseman, Sep 21 2020 STATUS approved

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Last modified April 11 14:44 EDT 2021. Contains 342886 sequences. (Running on oeis4.)