%I #7 May 31 2019 05:34:09
%S 1,2,6,30,42,210,330,390,462,510,546,714,798,2310,2730,3570,3990,4290,
%T 4830,5610,6006,6090,6270,6510,6630,7410,7590,7854,8778,8970,9282,
%U 9570,9690,10230,10374,10626,11310,11730,12090,12210,12558,13398,13566,14322,14430
%N Heinz numbers of complete strict integer partitions.
%C Strict partitions are counted by A000009, while complete partitions are counted by A126796.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C An integer partition of n is complete (A126796, A325781) if every number from 0 to n is the sum of some submultiset of the parts.
%C The enumeration of these partitions by sum is given by A188431.
%F Intersection of A005117 (strict partitions) and A325781 (complete partitions).
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 6: {1,2}
%e 30: {1,2,3}
%e 42: {1,2,4}
%e 210: {1,2,3,4}
%e 330: {1,2,3,5}
%e 390: {1,2,3,6}
%e 462: {1,2,4,5}
%e 510: {1,2,3,7}
%e 546: {1,2,4,6}
%e 714: {1,2,4,7}
%e 798: {1,2,4,8}
%e 2310: {1,2,3,4,5}
%e 2730: {1,2,3,4,6}
%e 3570: {1,2,3,4,7}
%e 3990: {1,2,3,4,8}
%e 4290: {1,2,3,5,6}
%e 4830: {1,2,3,4,9}
%e 5610: {1,2,3,5,7}
%t hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p] k]];
%t Select[Range[1000],SquareFreeQ[#]&&Union[hwt/@Divisors[#]]==Range[0,hwt[#]]&]
%Y Cf. A002033, A056239, A103295, A112798, A126796, A188431, A299702, A304793.
%Y Cf. A325780, A325781, A325782, A325788, A325790, A325988.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 30 2019
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