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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.
Sequence in context: A183912 A144693 A328399 * A029139 A100927 A001687
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.)