A318717 - OEIS

%I #15 Dec 24 2020 09:15:42

%S 1,1,1,1,1,1,2,1,2,2,3,1,5,1,5,4,6,1,10,1,11,6,12,1,19,3,18,8,23,1,36,

%T 2,32,13,38,7,57,2,54,19,68,3,95,3,90,33,104,3,148,7,149,40,166,5,230,

%U 17,226,56,256,6,360,9,340,84,390,25,527,11,513,109

%N Number of strict integer partitions of n in which no two parts are relatively prime.

%H Fausto A. C. Cariboni, <a href="/A318717/b318717.txt">Table of n, a(n) for n = 0..600</a>

%e The a(20) = 11 partitions:

%e   (20),

%e   (12,8), (14,6), (15,5), (16,4), (18,2),

%e   (10,6,4), (10,8,2), (12,6,2), (14,4,2),

%e   (8,6,4,2).

%t Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,And@@(GCD[##]>1&)@@@Select[Tuples[#,2],Less@@#&]]&]],{n,30}]

%Y Cf. A000009, A007359, A007360, A051185, A302569, A302797, A303140, A303280, A303283, A305713, A305843, A305854, A305713, A318715, A318719.

%K nonn

%O 0,7

%A _Gus Wiseman_, Sep 02 2018

%E a(51)-a(69) from _Alois P. Heinz_, Sep 02 2018