login
A280290
Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is even.
3
8, 9, 10, 11, 19, 21, 25, 27, 28, 30, 31, 34, 42, 45, 46, 47, 50, 55, 58, 59, 62, 64, 65, 66, 74, 75, 78, 79, 80, 84, 86, 94, 96, 97, 98, 101, 103, 106, 108, 109, 110, 112, 113, 116, 120, 122, 124, 125, 128, 129, 130, 131, 133, 135, 136, 137, 141, 142, 147, 149, 151, 153, 154, 158, 160, 163, 167, 170, 171, 174, 175, 179, 180
OFFSET
1,1
COMMENTS
Intersection of A001560 and A090864.
Numbers n such that A000035(A000041(n)) = 0 and A000035(A000009(n)) = 0.
EXAMPLE
8 is in the sequence because we have:
-----------------------------------
number of partitions = 22 (is even)
-----------------------------------
8 = 8
7 + 1 = 8
6 + 2 = 8
6 + 1 + 1 = 8
5 + 3 = 8
5 + 2 + 1 = 8
5 + 1 + 1 + 1 = 8
4 + 4 = 8
4 + 3 + 1 = 8
4 + 2 + 2 = 8
4 + 2 + 1 + 1 = 8
4 + 1 + 1 + 1 + 1 = 8
3 + 3 + 2 = 8
3 + 3 + 1 + 1 = 8
3 + 2 + 2 + 1 = 8
3 + 2 + 1 + 1 + 1 = 8
3 + 1 + 1 + 1 + 1 + 1 = 8
2 + 2 + 2 + 2 = 8
2 + 2 + 2 + 1 + 1 = 8
2 + 2 + 1 + 1 + 1 + 1 = 8
2 + 1 + 1 + 1 + 1 + 1 + 1 = 8
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
-------------------------------------------------------
number of partitions into distinct parts = 6 (is even)
-------------------------------------------------------
8 = 8
7 + 1 = 8
6 + 2 = 8
5 + 3 = 8
5 + 2 + 1 = 8
4 + 3 + 1 = 8
MATHEMATICA
Select[Range[180], Mod[PartitionsP[#1], 2] == Mod[PartitionsQ[#1], 2] == 0 & ]
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 31 2016
STATUS
approved