login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A319071 Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity. 4
1, 0, 0, 0, 2, 0, 2, 0, 3, 2, 3, 0, 4, 1, 4, 3, 7, 1, 7, 1, 8, 6, 8, 0, 15, 5, 12, 6, 15, 4, 22, 4, 24, 12, 22, 8, 35, 7, 30, 16, 42, 9, 50, 9, 50, 30, 53, 7, 79, 22, 72, 33, 87, 21, 109, 26, 111, 55, 117, 24, 168, 40, 149, 65, 178, 59 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The positions of zeros appear to be A048278.

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

The a(4) = 2 through a(16) = 7 integer partitions (G = 16):

  4   33   8     9    55     66      94  77       555     G

  22  222  44    333  3322   444         5522     33333   88

           2222       22222  3333        332222   333222  664

                             222222      2222222          4444

                                                          5533

                                                          333322

                                                          22222222

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], And[GCD@@FactorInteger[Times@@#][[All, 2]]>1, SameQ@@PrimeOmega/@#]&]], {n, 30}]

CROSSREFS

Cf. A003963, A048278, A064573, A279787, A305551, A319056, A319066, A319169, A320322, A320323.

Sequence in context: A144494 A136166 A259525 * A316432 A046522 A242896

Adjacent sequences:  A319068 A319069 A319070 * A319072 A319073 A319074

KEYWORD

nonn

AUTHOR

Gus Wiseman, Oct 10 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 June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)