%I #5 Sep 23 2019 13:43:40
%S 9,21,25,27,39,49,57,63,65,81,87,91,111,115,117,121,125,129,133,147,
%T 159,169,171,183,185,189,203,213,235,237,243,247,259,261,267,273,289,
%U 299,301,303,305,319,321,325,333,339,343,351,361,365,371,377,387,393,399
%N Nonprime numbers whose prime indices have a common divisor > 1.
%C First differs from A322336 in lacking 2535 = prime(2)*prime(3)*prime(6)^2.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Heinz numbers of integer partitions with a common divisor > 1 are A318978, and the enumeration of these partitions by sum is A108572.
%F Complement of A000040 in A318978.
%e The sequence of terms together with their prime indices begins:
%e 9: {2,2}
%e 21: {2,4}
%e 25: {3,3}
%e 27: {2,2,2}
%e 39: {2,6}
%e 49: {4,4}
%e 57: {2,8}
%e 63: {2,2,4}
%e 65: {3,6}
%e 81: {2,2,2,2}
%e 87: {2,10}
%e 91: {4,6}
%e 111: {2,12}
%e 115: {3,9}
%e 117: {2,2,6}
%e 121: {5,5}
%e 125: {3,3,3}
%e 129: {2,14}
%e 133: {4,8}
%e 147: {2,4,4}
%t Select[Range[100],#>1&&!PrimeQ[#]&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]
%Y Cf. A000837, A007916, A018783, A056239, A108572, A112798, A289509, A318978, A327407, A327658.
%K nonn
%O 1,1
%A _Gus Wiseman_, Sep 22 2019