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A325767 Heinz numbers of integer partitions covering an initial interval of positive integers and containing their own multiset of multiplicities (as a submultiset).

%I A325767 #7 May 21 2019 22:05:41
%S A325767 1,2,12,18,36,60,120,180,360,450,540,600,840,1260,1350,1500,1680,1800,
%T A325767 2250,2520,2700,3000,3780,4200,4500,5040,5400,5880,6750,8400,9000,
%U A325767 10500,11340,11760,12600,13500,15120,17640,18480,18900,20580,21000,22680,25200
%N A325767 Heinz numbers of integer partitions covering an initial interval of positive integers and containing their own multiset of multiplicities (as a submultiset).
%C A325767 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325767 The enumeration of these partitions by sum is given by A325766.
%e A325767 The sequence of terms together with their prime indices begins:
%e A325767      1: {}
%e A325767      2: {1}
%e A325767     12: {1,1,2}
%e A325767     18: {1,2,2}
%e A325767     36: {1,1,2,2}
%e A325767     60: {1,1,2,3}
%e A325767    120: {1,1,1,2,3}
%e A325767    180: {1,1,2,2,3}
%e A325767    360: {1,1,1,2,2,3}
%e A325767    450: {1,2,2,3,3}
%e A325767    540: {1,1,2,2,2,3}
%e A325767    600: {1,1,1,2,3,3}
%e A325767    840: {1,1,1,2,3,4}
%e A325767   1260: {1,1,2,2,3,4}
%e A325767   1350: {1,2,2,2,3,3}
%e A325767   1500: {1,1,2,3,3,3}
%e A325767   1680: {1,1,1,1,2,3,4}
%e A325767   1800: {1,1,1,2,2,3,3}
%e A325767   2250: {1,2,2,3,3,3}
%e A325767   2520: {1,1,1,2,2,3,4}
%t A325767 red[n_]:=If[n==1,1,Times@@Prime/@Last/@FactorInteger[n]];
%t A325767 Select[Range[1000],#==1||Range[PrimeNu[#]]==PrimePi/@First/@FactorInteger[#]&&Divisible[#,red[#]]&]
%Y A325767 Cf. A000009, A055932, A056239, A112798, A109297, A114640, A290689, A325702, A325708, A325766.
%K A325767 nonn
%O A325767 1,2
%A A325767 _Gus Wiseman_, May 19 2019