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 A328188 Number of strict integer partitions of n with all pairs of consecutive parts relatively prime. 10
 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 12, 15, 15, 19, 23, 25, 30, 35, 39, 47, 52, 58, 65, 75, 86, 95, 109, 124, 144, 165, 181, 203, 221, 249, 285, 316, 352, 392, 438, 484, 538, 599, 666, 737, 813, 899, 992, 1102, 1215, 1335, 1472, 1621, 1776, 1946, 2137, 2336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE The a(1) = 1 through a(15) = 15 partitions (A..F = 10..15):   1  2  3   4   5   6    7   8    9    A     B     C    D     E     F         21  31  32  51   43  53   54   73    65    75   76    95    87                 41  321  52  71   72   91    74    B1   85    B3    B4                          61  431  81   532   83    543  94    D1    D2                              521  432  541   92    651  A3    653   E1                                   531  721   A1    732  B2    743   654                                        4321  731   741  C1    752   753                                              5321  831  652   761   852                                                    921  751   851   951                                                         832   941   A32                                                         5431  A31   B31                                                         7321  B21   6531                                                               5432  7431                                                               6521  7521                                                               8321  54321 MAPLE b:= proc(n, i, s) option remember; `if`(i*(i+1)/2 igcd(i, j)=1, s), b(n-i, min(n-i, i-1),            numtheory[factorset](i)), 0)+b(n, i-1, s)))     end: a:= n-> b(n\$2, {}): seq(a(n), n=0..60);  # Alois P. Heinz, Oct 13 2019 MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MatchQ[#, {___, x_, y_, ___}/; GCD[x, y]>1]&]], {n, 0, 30}] CROSSREFS The case of compositions is A167606. The non-strict case is A328172. The Heinz numbers of these partitions are given by A328335. Partitions with no pairs of consecutive parts relatively prime are A328187. Cf. A000837, A018783, A178470, A328028, A328170, A328171, A328187, A328220. Sequence in context: A011881 A076678 A029024 * A106244 A029023 A140952 Adjacent sequences:  A328185 A328186 A328187 * A328189 A328190 A328191 KEYWORD nonn AUTHOR Gus Wiseman, Oct 13 2019 STATUS approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)