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A325986 Heinz numbers of complete strict integer partitions.

%I A325986 #7 May 31 2019 05:34:09
%S A325986 1,2,6,30,42,210,330,390,462,510,546,714,798,2310,2730,3570,3990,4290,
%T A325986 4830,5610,6006,6090,6270,6510,6630,7410,7590,7854,8778,8970,9282,
%U A325986 9570,9690,10230,10374,10626,11310,11730,12090,12210,12558,13398,13566,14322,14430
%N A325986 Heinz numbers of complete strict integer partitions.
%C A325986 Strict partitions are counted by A000009, while complete partitions are counted by A126796.
%C A325986 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325986 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 A325986 The enumeration of these partitions by sum is given by A188431.
%F A325986 Intersection of A005117 (strict partitions) and A325781 (complete partitions).
%e A325986 The sequence of terms together with their prime indices begins:
%e A325986       1: {}
%e A325986       2: {1}
%e A325986       6: {1,2}
%e A325986      30: {1,2,3}
%e A325986      42: {1,2,4}
%e A325986     210: {1,2,3,4}
%e A325986     330: {1,2,3,5}
%e A325986     390: {1,2,3,6}
%e A325986     462: {1,2,4,5}
%e A325986     510: {1,2,3,7}
%e A325986     546: {1,2,4,6}
%e A325986     714: {1,2,4,7}
%e A325986     798: {1,2,4,8}
%e A325986    2310: {1,2,3,4,5}
%e A325986    2730: {1,2,3,4,6}
%e A325986    3570: {1,2,3,4,7}
%e A325986    3990: {1,2,3,4,8}
%e A325986    4290: {1,2,3,5,6}
%e A325986    4830: {1,2,3,4,9}
%e A325986    5610: {1,2,3,5,7}
%t A325986 hwt[n_]:=Total[Cases[FactorInteger[n],{p_,k_}:>PrimePi[p] k]];
%t A325986 Select[Range[1000],SquareFreeQ[#]&&Union[hwt/@Divisors[#]]==Range[0,hwt[#]]&]
%Y A325986 Cf. A002033, A056239, A103295, A112798, A126796, A188431, A299702, A304793.
%Y A325986 Cf. A325780, A325781, A325782, A325788, A325790, A325988.
%K A325986 nonn
%O A325986 1,2
%A A325986 _Gus Wiseman_, May 30 2019