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

1, 2, 3, 30, 70, 2310, 180180, 21441420, 6401795400, 200984366583000, 41615822944675980000, 10515527757483671302380000, 4919824049783476260137727416400000, 5158181210492841550866520676965246284000000, 29776760895364738730693151196801613158042403043600000000

Offset: 0

Author

Gus Wiseman, May 07 2019

Keywords

• nonn

Comments

a(n) is the product of row n of A246867 (squarefree numbers arranged by sum of prime indices).

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Examples

			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.
The sequence of terms together with their prime indices begins:
                     1: {}
                     2: {1}
                     3: {2}
                    30: {1,2,3}
                    70: {1,3,4}
                  2310: {1,2,3,4,5}
                180180: {1,1,2,2,3,4,5,6}
              21441420: {1,1,2,2,3,4,4,5,6,7}
            6401795400: {1,1,1,2,2,3,3,4,5,5,6,7,8}
       200984366583000: {1,1,1,2,2,2,3,3,3,4,4,5,5,6,6,7,8,9}
  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}
		

Crossrefs

Cf. A003963, A006128, A015723, A022629, A056239, A112798, A147655, A215366, A246867, A325501, A325504, A325505, A325512, A325513.

Programs

Mathematica

Table[Times@@Prime/@(Join@@Select[IntegerPartitions[n],UnsameQ@@#&]),{n,0,15}]

Formula

a(n) = Product_{i = 1..A000009(n)} A246867(n,i).

A001222(a(n)) = A015723(n).

A056239(a(n)) = A066189(n).

A003963(a(n)) = A325504(n).

a(n) = A003963(A325505(n)).