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A325506 Product of Heinz numbers over all strict integer partitions of n. 9
1, 2, 3, 30, 70, 2310, 180180, 21441420, 6401795400, 200984366583000, 41615822944675980000, 10515527757483671302380000, 4919824049783476260137727416400000, 5158181210492841550866520676965246284000000, 29776760895364738730693151196801613158042403043600000000 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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).
LINKS
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)).
EXAMPLE
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}
MATHEMATICA
Table[Times@@Prime/@(Join@@Select[IntegerPartitions[n], UnsameQ@@#&]), {n, 0, 15}]
CROSSREFS
Sequence in context: A167453 A095927 A296248 * A203431 A137981 A110351
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 07 2019
STATUS
approved

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Last modified May 27 20:38 EDT 2024. Contains 372882 sequences. (Running on oeis4.)