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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 Table of n, a(n) for n=0..14. 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 Cf. A003963, A006128, A015723, A022629, A056239, A112798, A147655, A215366, A246867, A325501, A325504, A325505, A325512, A325513. Sequence in context: A167453 A095927 A296248 * A203431 A137981 A110351 Adjacent sequences: A325503 A325504 A325505 * A325507 A325508 A325509 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.)