A366853 Number of integer partitions of n into odd, pairwise coprime parts.

1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 18, 20, 22, 25, 29, 33, 36, 39, 43, 49, 55, 61, 66, 69, 75, 85, 94, 104, 113, 120, 129, 143, 159, 172, 183, 193, 207, 226, 251, 272, 288, 304, 325, 350, 383, 414, 437, 460, 494, 532, 577, 622, 655, 684

Offset: 0

Author

Gus Wiseman, Nov 01 2023

Keywords

• nonn

Examples

			The a(1) = 1 through a(10) = 7 partitions:
1  11  3    31    5      51      7        53        9          73
       111  1111  311    3111    511      71        531        91
                  11111  111111  31111    5111      711        5311
                                 1111111  311111    51111      7111
                                          11111111  3111111    511111
                                                    111111111  31111111
                                                               1111111111
		

Crossrefs

Partitions into odd parts are counted by A000009, ranks A066208.

Allowing even parts gives A051424.

For relatively prime (not pairwise coprime): A366843, with evens A000837.

A000041 counts integer partitions, strict A000009 (also into odds).

A101268 counts pairwise coprime compositions.

A168532 counts partitions by gcd.

Cf. A007359, A018783, A055922, A078374, A337485, A366844, A366852.

Programs

Mathematica

pwcop[y_]:=And@@(GCD@@#==1&)/@Subsets[y,{2}]
Table[Length[Select[IntegerPartitions[n],And@@OddQ/@#&&pwcop[#]&]],{n,0,30}]