A325501 Product of Heinz numbers over all integer partitions of n.

1, 2, 12, 240, 120960, 638668800, 15064408719360000, 27259975545259032576000000, 682714624600511148826789083611136000000000, 2948964060660649503322235948384635104494106968064000000000000000

Offset

0,2

Comments

Row-products of A215366 (positive integers arranged by sum of prime indices A056239).

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

Links

Table of n, a(n) for n=0..9.

Index entries for sequences related to Heinz numbers

Formula

A001222(a(n)) = A006128(n).

A056239(a(n)) = A066186(n).

A003963(a(n)) = A007870(n).

A124010(a(n),i) = A066633(n,i).

Example

The integer partitions of 3 are {(3), (2,1), (1,1,1)}, with Heinz numbers {5,6,8}, with product 240, so a(3) = 240.
The sequence of terms together with their prime indices begins:
          1: {}
          2: {1}
         12: {1,1,2}
        240: {1,1,1,1,2,3}
     120960: {1,1,1,1,1,1,1,2,2,2,3,4}
  638668800: {1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,3,3,4,5}

Mathematica

Table[Times@@Prime/@(Join@@IntegerPartitions[n]), {n, 0, 5}]

Crossrefs

Cf. A003963, A006128, A007870, A008284, A056239, A066186, A066633, A112798, A118914, A124010, A145519, A215366, A325500, A325506, A325507.

Sequence in context: A366350 A087046 A111403 * A007986 A013503 A231074

Adjacent sequences: A325498 A325499 A325500 * A325502 A325503 A325504

Keyword

nonn

Author

Gus Wiseman, May 06 2019

Status

approved