%I #13 Feb 12 2022 20:30:59

%S 0,0,0,1,0,1,0,2,1,1,0,4,0,1,1,5,0,4,0,8,1,1,0,14,1,1,3,16,0,10,0,22,

%T 1,1,1,41,0,1,1,45,0,18,0,57,9,1,0,94,1,8,1,102,0,38,1,138,1,1,0,221,

%U 0,1,17,231,1,59,0,298,1,22

%N Number of integer partitions of n whose greatest common divisor is composite (nonprime and > 1).

%H Andrew Howroyd, <a href="/A305736/b305736.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A018783(n) - A305735(n). - _Andrew Howroyd_, Jun 22 2018

%e The a(12) = 4 integer partitions are (12), (8 4), (6 6), (4 4 4).

%t Table[Length[Select[IntegerPartitions[n],!(GCD@@#==1||PrimeQ[GCD@@#])&]],{n,0,20}]

%o (PARI) seq(n)={dirmul(vector(n, n, numbpart(n)), dirmul(vector(n, n, moebius(n)), vector(n, n, n>1&&!isprime(n))))} \\ _Andrew Howroyd_, Jun 22 2018

%Y Cf. A000040, A000837, A018783, A100953, A289508, A302698, A305563, A305731, A305735.

%K nonn

%O 1,8

%A _Gus Wiseman_, Jun 22 2018