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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A324748 Number of strict integer partitions of n containing all prime indices of the parts. 10
 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 2, 3, 2, 2, 4, 3, 4, 3, 5, 6, 9, 8, 7, 8, 11, 12, 13, 15, 17, 22, 22, 20, 28, 31, 32, 36, 41, 43, 53, 53, 59, 70, 76, 77, 89, 99, 108, 124, 135, 139, 160, 172, 188, 209, 229, 243, 274, 298, 315, 353, 391, 417, 457, 496, 538, 588 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 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 EXAMPLE The first 15 terms count the following integer partitions.    1: (1)    3: (2,1)    5: (4,1)    6: (3,2,1)    7: (4,2,1)    9: (8,1)    9: (6,2,1)   10: (4,3,2,1)   11: (8,2,1)   11: (5,3,2,1)   12: (9,2,1)   12: (7,4,1)   12: (6,3,2,1)   13: (8,4,1)   13: (6,4,2,1)   14: (8,3,2,1)   14: (7,4,2,1)   15: (12,2,1)   15: (9,3,2,1)   15: (8,4,2,1)   15: (5,4,3,2,1) An example for n = 6 is (20,18,11,5,3,2,1), with prime indices:   20: {1,1,3}   18: {1,2,2}   11: {5}    5: {3}    3: {2}    2: {1}    1: {} All of these prime indices {1,2,3,5} belong to the partition, as required. MATHEMATICA Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&SubsetQ[#, PrimePi/@First/@Join@@FactorInteger/@DeleteCases[#, 1]]&]], {n, 0, 30}] CROSSREFS The subset version is A324736. The non-strict version is A324753. The Heinz number version is A290822. An infinite version is A324698. Cf. A000720, A001462, A007097, A074971, A078374, A112798, A276625, A279861, A290689, A290760, A305713. Cf. A324697, A324737, A324751. Sequence in context: A029267 A111725 A302257 * A320387 A304707 A112218 Adjacent sequences:  A324745 A324746 A324747 * A324749 A324750 A324751 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)