%I #13 Jan 19 2021 21:54:57
%S 1,1,2,2,3,2,5,2,6,4,9,2,15,2,17,10,23,2,39,2,46,18,58,2,95,8,103,31,
%T 139,2,219,3,232,59,299,22,452,4,492,104,645,5,920,5,1006,204,1258,8,
%U 1785,21,1994,302,2442,11,3366,71,3738,497,4570,18,6253,24,6849
%N Number of integer partitions of n in which no two distinct parts are relatively prime.
%C A partition with no two distinct parts relatively prime is said to be intersecting.
%H Fausto A. C. Cariboni, <a href="/A328673/b328673.txt">Table of n, a(n) for n = 0..350</a>
%F a(n > 0) = A200976(n) + 1.
%e The a(1) = 1 through a(10) = 9 partitions (A = 10):
%e 1 2 3 4 5 6 7 8 9 A
%e 11 111 22 11111 33 1111111 44 63 55
%e 1111 42 62 333 64
%e 222 422 111111111 82
%e 111111 2222 442
%e 11111111 622
%e 4222
%e 22222
%e 1111111111
%t Table[Length[Select[IntegerPartitions[n],And@@(GCD[##]>1&)@@@Subsets[Union[#],{2}]&]],{n,0,20}]
%Y The Heinz numbers of these partitions are A328867 (strict case is A318719).
%Y The relatively prime case is A328672.
%Y The strict case is A318717.
%Y The version for non-isomorphic multiset partitions is A319752.
%Y The version for set-systems is A305843.
%Y The version involving all parts (not just distinct ones) is A200976.
%Y Cf. A000837, A202425, A305148, A305854, A306006, A316476, A326910.
%K nonn
%O 0,3
%A _Gus Wiseman_, Oct 29 2019