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!)
 A305563 Number of reducible integer partitions of n. 26
 1, 2, 3, 4, 7, 7, 15, 16, 27, 30, 56, 56, 100, 105, 157, 188, 287, 303, 470, 524, 724, 850, 1197, 1339, 1856, 2135, 2814, 3305, 4360, 4951, 6532, 7561, 9563, 11195, 14165, 16328, 20631, 23866, 29471, 34320, 42336, 48672, 59872, 69139, 83625, 96911, 117153 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A multiset m whose distinct elements are m_1, m_2, ..., m_k with multiplicities y_1, y_2, ..., y_k is reducible if either m is of size 1 or gcd(m_1, ..., m_k) = 1 and the multiset {y_1, ..., y_k} is also reducible. LINKS EXAMPLE The a(6) = 7 reducible integer partitions are (6), (51), (411), (321), (3111), (21111), (111111). Missing from this list are (42), (33), (222), (2211). MATHEMATICA ptnredQ[y_]:=Or[Length[y]==1, And[GCD@@y==1, ptnredQ[Sort[Length/@Split[y], Greater]]]]; Table[Length[Select[IntegerPartitions[n], ptnredQ]], {n, 20}] CROSSREFS Cf. A007916, A071625, A181819, A182850, A182857, A275870, A304465, A304660, A304687, A304818, A305564, A305565, A305566. Sequence in context: A217254 A223488 A175686 * A054426 A054424 A297164 Adjacent sequences:  A305560 A305561 A305562 * A305564 A305565 A305566 KEYWORD nonn AUTHOR Gus Wiseman, Jun 05 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.

Last modified April 16 18:53 EDT 2021. Contains 343050 sequences. (Running on oeis4.)