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!)
 A338315 Number of integer partitions of n with no 1's whose distinct parts are pairwise coprime, where a singleton is not considered coprime unless it is (1). 4
 0, 0, 0, 0, 0, 1, 0, 3, 2, 4, 4, 10, 6, 15, 13, 16, 21, 31, 29, 43, 41, 50, 63, 79, 81, 99, 113, 129, 145, 179, 197, 228, 249, 284, 328, 363, 418, 472, 522, 581, 655, 741, 828, 921, 1008, 1123, 1259, 1407, 1546, 1709, 1889, 2077, 2292, 2554, 2799, 3061, 3369 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 COMMENTS The Heinz numbers of these partitions are given by A337987. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions. LINKS EXAMPLE The a(5) = 1 through a(13) = 15 partitions (empty column indicated by dot, A = 10, B = 11):   32   .  43    53    54     73     65      75      76           52    332   72     433    74      543     85           322         522    532    83      552     94                       3222   3322   92      732     A3                                     443     5322    B2                                     533     33222   544                                     722             553                                     3332            733                                     5222            922                                     32222           4333                                                     5332                                                     7222                                                     33322                                                     52222                                                     322222 MATHEMATICA Table[Length[Select[IntegerPartitions[n], !MemberQ[#, 1]&&CoprimeQ@@Union[#]&]], {n, 0, 30}] CROSSREFS A200976 is a pairwise non-coprime instead of pairwise coprime version. A304709 allows 1's, with strict case A305713 and Heinz numbers A304711. A318717 counts pairwise non-coprime strict partitions. A337485 is the strict version, with Heinz numbers A337984. A337987 gives the Heinz numbers of these partitions. A338317 considers singletons coprime, with Heinz numbers A338316. A007359 counts singleton or pairwise coprime partitions with no 1's. A327516 counts pairwise coprime partitions, ranked by A302696. A328673 counts partitions with no two distinct parts relatively prime. A337462 counts pairwise coprime compositions, ranked by A333227. A337561 counts pairwise coprime strict compositions. A337665 counts compositions whose distinct parts are pairwise coprime. A337667 counts pairwise non-coprime compositions, ranked by A337666. A337697 counts pairwise coprime compositions with no 1's. Cf. A051424, A101268, A220377, A302568, A328867, A333228, A337563. Sequence in context: A195472 A240538 A326923 * A240541 A073369 A021759 Adjacent sequences:  A338312 A338313 A338314 * A338316 A338317 A338318 KEYWORD nonn AUTHOR Gus Wiseman, Oct 23 2020 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 13 20:25 EDT 2021. Contains 345009 sequences. (Running on oeis4.)