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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<n, 0, `if`(n=0, 1,

      `if`(andmap(j-> 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.)