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A325513 Heinz number of the integer partition whose parts are the multiplicities in the multiset union of all strict integer partitions of n. 8
1, 2, 2, 8, 8, 32, 144, 432, 2160, 27000, 582120, 7623000, 336936600, 6740402760, 543454231320, 57619849046760, 4683793138766280, 412882704970215480, 88171665744392750520, 12780536107937124847320, 2685589660883755945879560, 942036670625665177379096280 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Also the Heinz number of row n of A015716 (with zeros removed).

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..21.

FORMULA

a(n) = A181819(A003963(A325505(n))).

A056239(a(n)) = A015723(n).

EXAMPLE

The strict integer partitions of 6 are {(6), (5,1), (4,2), (3,2,1)}, with multiset union {1,1,2,2,3,4,5,6}, with multiplicities (2,2,1,1,1,1), so a(6) = prime(1)^4*prime(2)^2 = 144.

The sequence of terms together with their prime indices begins:

               1: {}

               2: {1}

               2: {1}

               8: {1,1,1}

               8: {1,1,1}

              32: {1,1,1,1,1}

             144: {1,1,1,1,2,2}

             432: {1,1,1,1,2,2,2}

            2160: {1,1,1,1,2,2,2,3}

           27000: {1,1,1,2,2,2,3,3,3}

          582120: {1,1,1,2,2,2,3,4,4,5}

         7623000: {1,1,1,2,2,3,3,3,4,5,5}

       336936600: {1,1,1,2,2,3,3,4,5,5,6,7}

      6740402760: {1,1,1,2,2,3,4,4,4,6,6,7,8}

    543454231320: {1,1,1,2,2,3,4,4,5,6,7,8,9,10}

  57619849046760: {1,1,1,2,2,3,4,5,5,6,8,9,10,11,12}

MATHEMATICA

Table[Times@@Prime/@Length/@Split[Sort[Join@@Select[IntegerPartitions[n], UnsameQ@@#&]]], {n, 0, 15}]

CROSSREFS

Cf. A006128, A015716, A015723, A022629, A056239, A066633, A112798, A246867, A325500, A325504, A325506.

Sequence in context: A158302 A007083 A281019 * A144060 A230928 A016119

Adjacent sequences:  A325510 A325511 A325512 * A325514 A325515 A325516

KEYWORD

nonn

AUTHOR

Gus Wiseman, May 07 2019

STATUS

approved

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Last modified December 8 00:04 EST 2021. Contains 349590 sequences. (Running on oeis4.)