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 A328220 Number of strict integer partitions of n with no pair of consecutive parts relatively prime. 9
 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 3, 1, 5, 1, 5, 4, 6, 3, 10, 3, 11, 7, 12, 3, 19, 5, 18, 12, 23, 9, 36, 11, 33, 21, 40, 20, 58, 19, 58, 35, 70, 31, 98, 36, 101, 65, 112, 56, 155, 64, 164, 97, 188, 88, 250, 112, 256, 157, 293, 145, 392, 163, 399, 241, 461, 242 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS EXAMPLE The a(2) = 1 through a(20) = 11 partitions (A..K = 10..20):   2  3  4  5  6   7  8   9   A   B  C    D  E    F   G    H    I    J    K               42     62  63  64     84      86   96  A6   863  A8   964  C8                              82     93      A4   A5  C4   962  C6   A63  E6                                     A2      C2   C3  E2        E4        F5                                     642     842      862       F3        G4                                                      A42       G2        I2                                                                864       A64                                                                963       A82                                                                A62       C62                                                                C42       E42                                                                          8642 MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MatchQ[#, {___, x_, y_, ___}/; GCD[x, y]==1]&]], {n, 0, 30}] CROSSREFS The non-strict case is A328187. Partitions with all consecutive parts relatively prime are A328172, with strict case A328188. Strict partitions with relatively prime parts are A078374. Partitions with no consecutive divisibilities are A328171. Cf. A000837, A018783, A070211, A289509, A318980, A325545, A328170, A328221, A328335, A328336. Sequence in context: A303280 A318717 A331887 * A134192 A309342 A284044 Adjacent sequences:  A328217 A328218 A328219 * A328221 A328222 A328223 KEYWORD nonn AUTHOR Gus Wiseman, Oct 14 2019 STATUS approved

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Last modified April 9 12:51 EDT 2020. Contains 333352 sequences. (Running on oeis4.)