login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..17.

Index entries for sequences related to Heinz numbers

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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