cp's OEIS Frontend

A366844 Number of strict integer partitions of n into odd relatively prime parts.

%I A366844 #13 Oct 31 2023 02:24:21
%S A366844 0,1,0,0,1,0,1,0,2,1,2,1,2,2,3,3,5,4,4,5,6,7,8,8,9,11,12,12,15,16,15,
%T A366844 19,23,23,26,28,30,34,37,38,44,48,48,56,62,63,72,77,82,92,96,102,116,
%U A366844 124,128,142,155,162,178,191,200,222,236,246,276,291,303,334
%N A366844 Number of strict integer partitions of n into odd relatively prime parts.
%e A366844 The a(n) partitions for n = 1, 8, 14, 17, 16, 20, 21:
%e A366844   (1)  (5,3)  (9,5)   (9,5,3)   (9,7)      (11,9)      (9,7,5)
%e A366844        (7,1)  (11,3)  (9,7,1)   (11,5)     (13,7)      (11,7,3)
%e A366844               (13,1)  (11,5,1)  (13,3)     (17,3)      (11,9,1)
%e A366844                       (13,3,1)  (15,1)     (19,1)      (13,5,3)
%e A366844                                 (7,5,3,1)  (9,7,3,1)   (13,7,1)
%e A366844                                            (11,5,3,1)  (15,5,1)
%e A366844                                                        (17,3,1)
%t A366844 Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&UnsameQ@@#&&GCD@@#==1&]],{n,0,30}]
%o A366844 (Python)
%o A366844 from math import gcd
%o A366844 from sympy.utilities.iterables import partitions
%o A366844 def A366844(n): return sum(1 for p in partitions(n) if all(d==1 for d in p.values()) and all(d&1 for d in p) and gcd(*p)==1) # _Chai Wah Wu_, Oct 30 2023
%Y A366844 This is the relatively prime case of A000700.
%Y A366844 The pairwise coprime version is the odd-part case of A007360.
%Y A366844 Allowing even parts gives A078374.
%Y A366844 The halved even version is A078374 aerated.
%Y A366844 The non-strict version is A366843, with evens A000837.
%Y A366844 The complement is counted by the strict case of A366852, with evens A018783.
%Y A366844 A000041 counts integer partitions, strict A000009 (also into odds).
%Y A366844 A051424 counts pairwise coprime partitions, for odd parts A366853.
%Y A366844 A113685 counts partitions by sum of odd parts, rank statistic A366528.
%Y A366844 A168532 counts partitions by gcd.
%Y A366844 A366842 counts partitions whose odd parts have a common divisor > 1.
%Y A366844 Cf. A007359, A047967, A055922, A066208, A116598, A239261, A302697, A337485, A365067, A366845, A366848.
%K A366844 nonn
%O A366844 0,9
%A A366844 _Gus Wiseman_, Oct 29 2023
%E A366844 More terms from _Chai Wah Wu_, Oct 30 2023