A328171 - OEIS

A328171

Number of (necessarily strict) integer partitions of n with no two consecutive parts divisible.

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

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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