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 A328673 Number of integer partitions of n in which no two distinct parts are relatively prime. 5
 1, 1, 2, 2, 3, 2, 5, 2, 6, 4, 9, 2, 15, 2, 17, 10, 23, 2, 39, 2, 46, 18, 58, 2, 95, 8, 103, 31, 139, 2, 219, 3, 232, 59, 299, 22, 452, 4, 492, 104, 645, 5, 920, 5, 1006, 204, 1258, 8, 1785, 21, 1994, 302, 2442, 11, 3366, 71, 3738, 497, 4570, 18, 6253, 24, 6849 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A partition with no two distinct parts relatively prime is said to be intersecting. LINKS FORMULA a(n > 0) = A200976(n) + 1. EXAMPLE The a(1) = 1 through a(10) = 9 partitions (A = 10):   1  2   3    4     5      6       7        8         9          A      11  111  22    11111  33      1111111  44        63         55               1111         42               62        333        64                            222              422       111111111  82                            111111           2222                 442                                             11111111             622                                                                  4222                                                                  22222                                                                  1111111111 MATHEMATICA Table[Length[Select[IntegerPartitions[n], And@@(GCD[##]>1&)@@@Subsets[Union[#], {2}]&]], {n, 0, 20}] CROSSREFS The Heinz numbers of these partitions are A328867 (strict case is A318719). The relatively prime case is A328672. The strict case is A318717. The version for non-isomorphic multiset partitions is A319752. The version for set-systems is A305843. The version involving all parts (not just distinct ones) is A200976. Cf. A000837, A202425, A305148, A305854, A306006, A316476, A326910. Sequence in context: A062830 A322366 A164941 * A115119 A066656 A164896 Adjacent sequences:  A328670 A328671 A328672 * A328674 A328675 A328676 KEYWORD nonn AUTHOR Gus Wiseman, Oct 29 2019 STATUS approved

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Last modified February 23 16:23 EST 2020. Contains 332177 sequences. (Running on oeis4.)