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A325762 Heinz numbers of integer partitions with no part greater than the number of ones.

%I A325762 #4 May 18 2019 22:46:58
%S A325762 1,2,4,8,12,16,24,32,36,40,48,64,72,80,96,108,112,120,128,144,160,192,
%T A325762 200,216,224,240,256,288,320,324,336,352,360,384,400,432,448,480,512,
%U A325762 560,576,600,640,648,672,704,720,768,784,800,832,864,896,960,972,1000
%N A325762 Heinz numbers of integer partitions with no part greater than the number of ones.
%C A325762 After 1 and 2, first differs from A322136 in having 200.
%C A325762 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325762 The enumeration of these partitions by sum is given by A002865.
%e A325762 The sequence of terms together with their prime indices begins:
%e A325762      1: {}
%e A325762      2: {1}
%e A325762      4: {1,1}
%e A325762      8: {1,1,1}
%e A325762     12: {1,1,2}
%e A325762     16: {1,1,1,1}
%e A325762     24: {1,1,1,2}
%e A325762     32: {1,1,1,1,1}
%e A325762     36: {1,1,2,2}
%e A325762     40: {1,1,1,3}
%e A325762     48: {1,1,1,1,2}
%e A325762     64: {1,1,1,1,1,1}
%e A325762     72: {1,1,1,2,2}
%e A325762     80: {1,1,1,1,3}
%e A325762     96: {1,1,1,1,1,2}
%e A325762    108: {1,1,2,2,2}
%e A325762    112: {1,1,1,1,4}
%e A325762    120: {1,1,1,2,3}
%e A325762    128: {1,1,1,1,1,1,1}
%e A325762    144: {1,1,1,1,2,2}
%t A325762 Select[Range[100],#==1||EvenQ[#]&&PrimePi[FactorInteger[#][[-1,1]]]<=FactorInteger[#][[1,2]]&]
%Y A325762 Cf. A001222, A002865, A007814, A056239, A061395, A093641, A109298, A110295, A112798, A118914, A325761, A325763.
%K A325762 nonn
%O A325762 1,2
%A A325762 _Gus Wiseman_, May 18 2019