

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
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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.


KEYWORD

nonn


AUTHOR



STATUS

approved



