cp's OEIS Frontend

A366843 Number of integer partitions of n into odd, relatively prime parts.

%I A366843 #10 Oct 31 2023 04:34:58
%S A366843 1,1,1,1,2,2,3,4,6,6,9,11,13,17,21,23,32,37,42,53,62,70,88,103,116,
%T A366843 139,164,184,220,255,283,339,390,435,511,578,653,759,863,963,1107,
%U A366843 1259,1401,1609,1814,2015,2303,2589,2878,3259,3648,4058,4580,5119,5672,6364
%N A366843 Number of integer partitions of n into odd, relatively prime parts.
%e A366843 The a(1) = 1 through a(8) = 6 partitions:
%e A366843   (1)  (11)  (111)  (31)    (311)    (51)      (331)      (53)
%e A366843                     (1111)  (11111)  (3111)    (511)      (71)
%e A366843                                      (111111)  (31111)    (3311)
%e A366843                                                (1111111)  (5111)
%e A366843                                                           (311111)
%e A366843                                                           (11111111)
%t A366843 Table[Length[Select[IntegerPartitions[n],#=={}||And@@OddQ/@#&&GCD@@#==1&]],{n,0,30}]
%o A366843 (Python)
%o A366843 from math import gcd
%o A366843 from sympy.utilities.iterables import partitions
%o A366843 def A366843(n): return sum(1 for p in partitions(n) if all(d&1 for d in p) and gcd(*p)==1) # _Chai Wah Wu_, Oct 30 2023
%Y A366843 Allowing even parts gives A000837.
%Y A366843 The strict case is A366844, with evens A078374.
%Y A366843 The complement is counted by A366852, with evens A018783.
%Y A366843 The pairwise coprime version is A366853, with evens A051424.
%Y A366843 A000041 counts integer partitions, strict A000009 (also into odds).
%Y A366843 A000740 counts relatively prime compositions.
%Y A366843 A168532 counts partitions by gcd.
%Y A366843 A366842 counts partitions whose odd parts have a common divisor > 1.
%Y A366843 Cf. A007359, A047967, A055922, A066208, A113685, A116598, A289509, A289508, A302697, A337485, A366845, A366848, A366849.
%K A366843 nonn
%O A366843 0,5
%A A366843 _Gus Wiseman_, Oct 28 2023