login
A366850
Number of integer partitions of n whose odd parts are relatively prime.
7
0, 1, 1, 2, 3, 5, 7, 11, 16, 22, 32, 43, 60, 80, 110, 140, 194, 244, 327, 410, 544, 670, 883, 1081, 1401, 1708, 2195, 2651, 3382, 4069, 5129, 6157, 7708, 9194, 11438, 13599, 16788, 19911, 24432, 28858, 35229, 41507, 50359, 59201, 71489, 83776, 100731, 117784
OFFSET
0,4
EXAMPLE
The a(1) = 1 through a(8) = 16 partitions:
(1) (11) (21) (31) (41) (51) (61) (53)
(111) (211) (221) (321) (331) (71)
(1111) (311) (411) (421) (431)
(2111) (2211) (511) (521)
(11111) (3111) (2221) (611)
(21111) (3211) (3221)
(111111) (4111) (3311)
(22111) (4211)
(31111) (5111)
(211111) (22211)
(1111111) (32111)
(41111)
(221111)
(311111)
(2111111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@Select[#, OddQ]==1&]], {n, 0, 30}]
CROSSREFS
For all parts (not just odd) we have A000837, complement A018783.
The complement is counted by A366842.
These partitions have ranks A366846.
A000041 counts integer partitions, strict A000009 (also into odds).
A000740 counts relatively prime compositions.
A078374 counts relatively prime strict partitions.
A113685 counts partitions by sum of odd parts, rank statistic A366528.
A168532 counts partitions by gcd.
A239261 counts partitions with (sum of odd parts) = (sum of even parts).
Sequence in context: A241725 A022480 A308927 * A024791 A373298 A178240
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 28 2023
STATUS
approved