

A328871


Number of integer partitions of n whose distinct parts are pairwise indivisible (stable) and pairwise nonrelatively 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
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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.
Intersecting partitions are A328673.


KEYWORD

nonn


AUTHOR



STATUS

approved



