login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A324749 Number of strict integer partitions of n containing no part > 1 whose prime indices all belong to the partition. 6
1, 1, 1, 1, 2, 1, 3, 4, 3, 4, 6, 6, 8, 11, 10, 14, 14, 19, 21, 26, 28, 35, 38, 44, 50, 60, 65, 79, 88, 98, 113, 131, 144, 165, 185, 211, 234, 268, 297, 334, 374, 420, 470, 525, 584, 649, 727, 801, 902, 998, 1100, 1220, 1357, 1500, 1657, 1833, 2029, 2220, 2462 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

LINKS

Table of n, a(n) for n=0..58.

EXAMPLE

The a(0) = 1 through a(10) = 6 strict integer partitions:

() (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

(3,1) (4,2) (4,3) (6,2) (5,4) (6,4)

(5,1) (5,2) (7,1) (6,3) (7,3)

(6,1) (7,2) (8,2)

(9,1)

(6,3,1)

MATHEMATICA

Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!MemberQ[#, k_/; SubsetQ[#, PrimePi/@First/@FactorInteger[k]]]&]], {n, 0, 30}]

CROSSREFS

The subset version is A324738. The non-strict version is A324754. The Heinz number version is A324759. An infinite version is A324694.

Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A290822, A305713.

Cf. A324744, A324750, A324755, A324760.

Sequence in context: A122530 A301453 A278340 * A022466 A144254 A133310

Adjacent sequences: A324746 A324747 A324748 * A324750 A324751 A324752

KEYWORD

nonn

AUTHOR

Gus Wiseman, Mar 15 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 24 04:28 EDT 2023. Contains 361454 sequences. (Running on oeis4.)