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A325782 Heinz numbers of strict perfect integer partitions.

%I A325782 #7 Jan 22 2023 20:50:22
%S A325782 1,2,6,42,798,42294,5540514,1723099854,1238908795026,2005793339147094,
%T A325782 7363267348008982074,60091624827101302705914,
%U A325782 1073416694286510570235741782,41726927156999525396773990291686,3505771238949629125260760342336582662
%N A325782 Heinz numbers of strict perfect integer partitions.
%C A325782 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325782 The sum of prime indices of n is A056239(n). A number is in this sequence iff it is squarefree, all of its divisors have distinct sums of prime indices, and these sums cover an initial interval of nonnegative integers. For example, the divisors of 42 are {1, 2, 3, 6, 7, 14, 21, 42}, with respective sums of prime indices {0, 1, 2, 3, 4, 5, 6, 7}, so 42 is in the sequence.
%F A325782 a(n) = Product_{i = 0..n-1} prime(2^i).
%e A325782 The sequence of terms together with their prime indices begins:
%e A325782       1: {}
%e A325782       2: {1}
%e A325782       6: {1,2}
%e A325782      42: {1,2,4}
%e A325782     798: {1,2,4,8}
%e A325782   42294: {1,2,4,8,16}
%t A325782 Table[Times@@Prime[2^Range[0,n-1]],{n,0,10}]
%Y A325782 A subsequence of A005117, A299702, and A325781.
%Y A325782 Cf. A002033, A056239, A108917, A112798, A126796, A188431, A325780.
%K A325782 nonn
%O A325782 1,2
%A A325782 _Gus Wiseman_, May 21 2019