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A325506 Product of Heinz numbers over all strict integer partitions of n.

%I A325506 #7 May 07 2019 23:14:25
%S A325506 1,2,3,30,70,2310,180180,21441420,6401795400,200984366583000,
%T A325506 41615822944675980000,10515527757483671302380000,
%U A325506 4919824049783476260137727416400000,5158181210492841550866520676965246284000000,29776760895364738730693151196801613158042403043600000000
%N A325506 Product of Heinz numbers over all strict integer partitions of n.
%C A325506 a(n) is the product of row n of A246867 (squarefree numbers arranged by sum of prime indices).
%C A325506 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%F A325506 a(n) = Product_{i = 1..A000009(n)} A246867(n,i).
%F A325506 A001222(a(n)) = A015723(n).
%F A325506 A056239(a(n)) = A066189(n).
%F A325506 A003963(a(n)) = A325504(n).
%F A325506 a(n) = A003963(A325505(n)).
%e A325506 The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)}, with Heinz numbers {13,22,21,30}, with product 13*22*21*30 = 180180, so a(6) = 180180.
%e A325506 The sequence of terms together with their prime indices begins:
%e A325506                      1: {}
%e A325506                      2: {1}
%e A325506                      3: {2}
%e A325506                     30: {1,2,3}
%e A325506                     70: {1,3,4}
%e A325506                   2310: {1,2,3,4,5}
%e A325506                 180180: {1,1,2,2,3,4,5,6}
%e A325506               21441420: {1,1,2,2,3,4,4,5,6,7}
%e A325506             6401795400: {1,1,1,2,2,3,3,4,5,5,6,7,8}
%e A325506        200984366583000: {1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9}
%e A325506   41615822944675980000: {1,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,5,5,6,6,7,7,8,9,10}
%t A325506 Table[Times@@Prime/@(Join@@Select[IntegerPartitions[n],UnsameQ@@#&]),{n,0,15}]
%Y A325506 Cf. A003963, A006128, A015723, A022629, A056239, A112798, A147655, A215366, A246867, A325501, A325504, A325505, A325512, A325513.
%K A325506 nonn
%O A325506 0,2
%A A325506 _Gus Wiseman_, May 07 2019