%I #4 May 18 2019 22:46:58
%S 1,2,4,8,12,16,24,32,36,40,48,64,72,80,96,108,112,120,128,144,160,192,
%T 200,216,224,240,256,288,320,324,336,352,360,384,400,432,448,480,512,
%U 560,576,600,640,648,672,704,720,768,784,800,832,864,896,960,972,1000
%N Heinz numbers of integer partitions with no part greater than the number of ones.
%C After 1 and 2, first differs from A322136 in having 200.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C The enumeration of these partitions by sum is given by A002865.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 4: {1,1}
%e 8: {1,1,1}
%e 12: {1,1,2}
%e 16: {1,1,1,1}
%e 24: {1,1,1,2}
%e 32: {1,1,1,1,1}
%e 36: {1,1,2,2}
%e 40: {1,1,1,3}
%e 48: {1,1,1,1,2}
%e 64: {1,1,1,1,1,1}
%e 72: {1,1,1,2,2}
%e 80: {1,1,1,1,3}
%e 96: {1,1,1,1,1,2}
%e 108: {1,1,2,2,2}
%e 112: {1,1,1,1,4}
%e 120: {1,1,1,2,3}
%e 128: {1,1,1,1,1,1,1}
%e 144: {1,1,1,1,2,2}
%t Select[Range[100],#==1||EvenQ[#]&&PrimePi[FactorInteger[#][[-1,1]]]<=FactorInteger[#][[1,2]]&]
%Y Cf. A001222, A002865, A007814, A056239, A061395, A093641, A109298, A110295, A112798, A118914, A325761, A325763.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 18 2019