A280290 Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is even.

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.

Links

Table of n, a(n) for n=1..73.

Eric Weisstein's World of Mathematics, Partition Function P, Partition Function Q

Index entries for related partition-counting sequences

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 & ]

Crossrefs

Cf. A000009, A000035, A000041, A001560, A090864, A280288, A280289, A280291.

Sequence in context: A296701 A297134 A247455 * A138581 A323062 A097363

Adjacent sequences: A280287 A280288 A280289 * A280291 A280292 A280293

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 31 2016

Status

approved