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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319000 Regular triangle where T(n,k) is the number of finite multisets of positive integers with product n and sum k. 15
1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 3, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 3, 3, 3, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,10

LINKS

Table of n, a(n) for n=1..87.

EXAMPLE

Triangle begins:

  1

  0 1

  0 0 1

  0 0 0 2

  0 0 0 0 1

  0 0 0 0 1 2

  0 0 0 0 0 0 1

  0 0 0 0 0 2 2 3

  0 0 0 0 0 1 1 1 2

  0 0 0 0 0 0 1 1 1 2

  0 0 0 0 0 0 0 0 0 0 1

  0 0 0 0 0 0 2 3 3 3 3 4

  0 0 0 0 0 0 0 0 0 0 0 0 1

  0 0 0 0 0 0 0 0 1 1 1 1 1 2

  0 0 0 0 0 0 0 1 1 1 1 1 1 1 2

  0 0 0 0 0 0 0 3 3 4 4 4 4 4 4 5

  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

  0 0 0 0 0 0 0 1 2 2 3 3 3 3 3 3 3 4

  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

  0 0 0 0 0 0 0 0 2 2 2 3 3 3 3 3 3 3 3 4

Row 12 {0,0,0,0,0,0,2,3,3,3,3,4} corresponds to the partitions (C = 12):

. . . . . . (43)  (62)   (621)   (6211)   (62111)    (C)

            (322) (431)  (4311)  (43111)  (431111)   (621111)

                  (3221) (32211) (322111) (3221111)  (4311111)

                                          (32211111)

MATHEMATICA

Table[Length[Select[IntegerPartitions[k], Times@@#==n&]], {n, 20}, {k, n}]

CROSSREFS

Row sums are A319916. Column sums are A319005. Last column is A001055.

Cf. A000041, A002865, A069016, A096276, A301987, A318950, A319057.

Sequence in context: A112765 A105966 A318950 * A083915 A083892 A089814

Adjacent sequences:  A318997 A318998 A318999 * A319001 A319002 A319003

KEYWORD

nonn,tabl

AUTHOR

Gus Wiseman, Oct 22 2018

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 October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)