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 A328171 Number of (necessarily strict) integer partitions of n with no two consecutive parts divisible. 25
 1, 1, 1, 1, 1, 2, 1, 3, 2, 4, 4, 5, 4, 9, 9, 10, 12, 14, 16, 20, 23, 29, 34, 38, 41, 51, 60, 66, 78, 89, 103, 119, 137, 157, 180, 201, 229, 261, 298, 338, 379, 431, 486, 547, 618, 694, 783, 876, 986, 1103, 1241, 1387, 1551, 1728, 1932, 2148, 2395, 2664, 2963 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS EXAMPLE The a(1) = 1 through a(15) = 10 partitions (A..F = 10..15):   1  2  3  4  5   6  7   8   9    A    B   C    D    E     F               32     43  53  54   64   65  75   76   86    87                      52      72   73   74  543  85   95    96                              432  532  83  732  94   A4    B4                                        92       A3   B3    D2                                                 B2   653   654                                                 643  743   753                                                 652  752   852                                                 832  5432  A32                                                            6432 MATHEMATICA Table[Length[Select[IntegerPartitions[n], !MatchQ[#, {___, x_, y_, ___}/; Divisible[x, y]]&]], {n, 0, 30}] CROSSREFS The complement is counted by A328221. The Heinz numbers of these partitions are A328603. Partitions whose pairs of consecutive parts are relatively prime are A328172, with strict case A328188. Partitions with no pair of consecutive parts relatively prime are A328187, with strict case A328220. Numbers without consecutive divisible proper divisors are A328028. Cf. A000837, A018783, A328026, A328161, A328189, A328194, A328195. Sequence in context: A183912 A144693 A328399 * A029139 A100927 A001687 Adjacent sequences:  A328168 A328169 A328170 * A328172 A328173 A328174 KEYWORD nonn AUTHOR Gus Wiseman, Oct 11 2019 STATUS approved

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Last modified February 23 04:49 EST 2020. Contains 332159 sequences. (Running on oeis4.)