

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
(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

Table of n, a(n) for n=0..60.


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.
Cf. A000837, A285573, A303362, A305148, A316476, A328671, A328677.
Sequence in context: A076640 A326198 A324105 * A169819 A134681 A218703
Adjacent sequences: A328868 A328869 A328870 * A328872 A328873 A328874


KEYWORD

nonn


AUTHOR

Gus Wiseman, Nov 12 2019


STATUS

approved



