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 A328171 Number of (necessarily strict) integer partitions of n with no two consecutive parts divisible. 33
 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 Fausto A. C. Cariboni, Table of n, a(n) for n = 0..330 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 June 20 18:00 EDT 2024. Contains 373532 sequences. (Running on oeis4.)