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 A328187 Number of integer partitions of n with no pair of consecutive parts relatively prime. 12
 1, 1, 1, 1, 2, 1, 4, 1, 5, 3, 8, 1, 14, 1, 16, 9, 22, 3, 38, 4, 46, 19, 58, 9, 94, 18, 106, 41, 144, 28, 221, 37, 246, 92, 318, 87, 465, 95, 530, 198, 693, 169, 963, 220, 1108, 424, 1383, 381, 1899, 492, 2216, 815, 2732, 799, 3644, 1041, 4231, 1585, 5194, 1608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS EXAMPLE The a(1) = 1 through a(15) = 9 partitions (A..F = 10..15):   1  2  3  4   5  6    7  8     9    A      B  C       D  E        F            22     33      44    63   55        66         77       96                   42      62    333  64        84         86       A5                   222     422        82        93         A4       C3                           2222       442       A2         C2       555                                      622       444        644      663                                      4222      633        662      933                                      22222     642        842      6333                                                822        A22      33333                                                3333       4442                                                4422       6422                                                6222       8222                                                42222      44222                                                222222     62222                                                           422222                                                           2222222 MATHEMATICA Table[Length[Select[IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; GCD[x, y]==1]&]], {n, 0, 30}] CROSSREFS The Heinz numbers of these partitions are given by A328336. The case of compositions is A178470. The strict case is A328220. Partitions with all pairs of consecutive parts relatively prime are A328172. Cf. A000837, A018783, A328028, A328170, A328171, A328188. Sequence in context: A083711 A018783 A200976 * A331885 A298971 A328602 Adjacent sequences:  A328184 A328185 A328186 * A328188 A328189 A328190 KEYWORD nonn AUTHOR Gus Wiseman, Oct 12 2019 STATUS approved

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Last modified April 8 12:50 EDT 2020. Contains 333314 sequences. (Running on oeis4.)