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 A325507 Heinz number of the integer partition whose parts are the multiplicities in the multiset union of all integer partitions of n. 4
 1, 2, 6, 28, 340, 3108, 106932, 2732340, 236790060, 19703562780, 3419598096420, 674127752953380, 264134168649181380, 95825592671995399620, 67662122741507082338220, 50556978553034312461203420, 69259146896604886347745839660, 104191622563656655781003976625020 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Also the Heinz number of row n of A066633. The Heinz number of an integer partition or sequence (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS FORMULA a(n) = Product_{i = 1..n} prime(A066633(n,i)). a(n) = A181819(A003963(A325500(n))). a(n) = A181819(A325501(n)). A001222(a(n)) = n. A056239(a(n)) = A006128(n). For n > 0, A181819(a(n)) = A087009(n + 1). EXAMPLE The integer partitions of 4 are {(4), (3,1), (2,2), (2,1,1), (1,1,1,1)}, with multiset union {1,1,1,1,1,1,1,2,2,2,3,4}, with multiplicities (7,3,1,1), so a(4) = prime(7)*prime(3)*prime(1)*prime(1) = 340. The sequence of terms together with their prime indices begins:                         1: {}                         2: {1}                         6: {1,2}                        28: {1,1,4}                       340: {1,1,3,7}                      3108: {1,1,2,4,12}                    106932: {1,1,2,4,8,19}                   2732340: {1,1,2,3,6,11,30}                 236790060: {1,1,2,3,6,9,19,45}               19703562780: {1,1,2,3,5,8,15,26,67}             3419598096420: {1,1,2,3,5,8,13,21,41,97}           674127752953380: {1,1,2,3,5,7,12,18,31,56,139}        264134168649181380: {1,1,2,3,5,7,12,17,28,45,83,195}      95825592671995399620: {1,1,2,3,5,7,11,16,25,38,63,112,272}   67662122741507082338220: {1,1,2,3,5,7,11,16,24,35,55,87,160,373} MATHEMATICA Table[Times@@Prime/@Length/@Split[Sort[Join@@IntegerPartitions[n]]], {n, 0, 15}] CROSSREFS Cf. A001222, A003963, A006128, A007870, A056239, A066633, A087009, A112798, A215366, A302246, A325500, A325501, A325513. Sequence in context: A126340 A277480 A108800 * A306793 A326359 A136639 Adjacent sequences:  A325504 A325505 A325506 * A325508 A325509 A325510 KEYWORD nonn AUTHOR Gus Wiseman, May 07 2019 STATUS approved

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Last modified September 15 04:05 EDT 2019. Contains 327062 sequences. (Running on oeis4.)