OFFSET
0,5
EXAMPLE
The partition y = (6,4) has halved even parts (3,2) which are relatively prime, so y is counted under a(10).
The a(2) = 1 through a(9) = 15 partitions:
(2) (21) (22) (32) (42) (52) (62) (72)
(211) (221) (222) (322) (332) (432)
(2111) (321) (421) (422) (522)
(2211) (2221) (521) (621)
(21111) (3211) (2222) (3222)
(22111) (3221) (3321)
(211111) (4211) (4221)
(22211) (5211)
(32111) (22221)
(221111) (32211)
(2111111) (42111)
(222111)
(321111)
(2211111)
(21111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], GCD@@Select[#, EvenQ]/2==1&]], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 28 2023
STATUS
approved