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A366853
Number of integer partitions of n into odd, pairwise coprime parts.
3
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
0,4
EXAMPLE
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
MATHEMATICA
pwcop[y_]:=And@@(GCD@@#==1&)/@Subsets[y, {2}]
Table[Length[Select[IntegerPartitions[n], And@@OddQ/@#&&pwcop[#]&]], {n, 0, 30}]
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.
Sequence in context: A025764 A237119 A011881 * A076678 A029024 A328188
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 01 2023
STATUS
approved