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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 19 01:25 EDT 2019. Contains 328211 sequences. (Running on oeis4.)