OFFSET
1,1
COMMENTS
These partitions are defined to have an odd number of odd parts and an odd number of even parts. They also have even length and odd sum.
EXAMPLE
The sequence of partitions together with their Heinz numbers begins:
6: (2,1) 74: (12,1) 141: (15,2)
14: (4,1) 77: (5,4) 142: (20,1)
15: (3,2) 86: (14,1) 143: (6,5)
24: (2,1,1,1) 93: (11,2) 145: (10,3)
26: (6,1) 95: (8,3) 150: (3,3,2,1)
33: (5,2) 96: (2,1,1,1,1,1) 152: (8,1,1,1)
35: (4,3) 104: (6,1,1,1) 158: (22,1)
38: (8,1) 106: (16,1) 161: (9,4)
51: (7,2) 119: (7,4) 177: (17,2)
54: (2,2,2,1) 122: (18,1) 178: (24,1)
56: (4,1,1,1) 123: (13,2) 185: (12,3)
58: (10,1) 126: (4,2,2,1) 201: (19,2)
60: (3,2,1,1) 132: (5,2,1,1) 202: (26,1)
65: (6,3) 135: (3,2,2,2) 204: (7,2,1,1)
69: (9,2) 140: (4,3,1,1) 209: (8,5)
MATHEMATICA
primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], OddQ[Count[primeMS[#], _?EvenQ]]&&OddQ[Count[primeMS[#], _?OddQ]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Feb 15 2021
STATUS
approved