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A328871 Number of integer partitions of n whose distinct parts are pairwise indivisible (stable) and pairwise non-relatively prime (intersecting). 1
1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 2, 6, 2, 7, 5, 7, 2, 10, 2, 11, 7, 14, 2, 16, 4, 19, 8, 22, 2, 30, 3, 29, 14, 37, 8, 48, 4, 50, 19, 59, 5, 82, 4, 81, 28, 93, 8, 128, 9, 128, 38, 147, 8, 199, 19, 196, 52, 223, 12, 308 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A partition with no two distinct parts divisible is said to be stable, and a partition with no two distinct parts relatively prime is said to be intersecting, so these are just stable intersecting partitions.
LINKS
EXAMPLE
The a(1) = 1 through a(10) = 5 partitions (A = 10):
1 2 3 4 5 6 7 8 9 A
11 111 22 11111 33 1111111 44 333 55
1111 222 2222 111111111 64
111111 11111111 22222
1111111111
MATHEMATICA
stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];
Table[Length[Select[IntegerPartitions[n], stableQ[Union[#], Divisible]&&stableQ[Union[#], GCD[#1, #2]==1&]&]], {n, 0, 30}]
CROSSREFS
The Heinz numbers of these partitions are A329366.
Replacing "intersecting" with "relatively prime" gives A328676.
Stable partitions are A305148.
Intersecting partitions are A328673.
Sequence in context: A076640 A326198 A324105 * A169819 A134681 A218703
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 12 2019
STATUS
approved

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Last modified April 23 03:29 EDT 2024. Contains 371906 sequences. (Running on oeis4.)