A280288 Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is odd.

2, 15, 22, 26, 40, 57, 70, 100, 117, 126, 176, 187, 247, 260, 532, 551, 590, 651, 715, 782, 925, 950, 1001, 1027, 1080, 1107, 1162, 1276, 1365, 1457, 1520, 1552, 1650, 1751, 1820, 1926, 2072, 2185, 2262, 2301, 2380, 2420, 2501, 2667, 2752, 2926, 3015, 3060, 3151, 3290, 3432, 3577, 3725, 3927, 4082, 4187, 4240, 4401

Offset

1,1

Comments

Intersection of A001318 and A001560.

Numbers n such that A000035(A000041(n)) = 0 and A000035(A000009(n)) = 1.

Links

Table of n, a(n) for n=1..58.

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

Index entries for related partition-counting sequences

Example

15 is in the sequence because we have:
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number of partitions = 176 (is even)
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15 = 15
14 + 1 = 15
13 + 2 = 15
13 + 1 + 1 = 15
12 + 3 = 15
12 + 2 + 1 = 15
12 + 1 + 1 + 1 = 15
11 + 4 = 15
11 + 3 + 1 = 15
11 + 2 + 2 = 15
11 + 2 + 1 + 1 = 15
11 + 1 + 1 + 1 + 1 = 15
...
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number of partitions into distinct parts = 27 (is odd)
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15 = 15
14 + 1 = 15
13 + 2 = 15
12 + 3 = 15
12 + 2 + 1 = 15
11 + 4 = 15
11 + 3 + 1 = 15
10 + 5 = 15
10 + 4 + 1 = 15
10 + 3 + 2 = 15
...

Mathematica

Select[Range[4500], Mod[PartitionsP[#1], 2] == 0 && Mod[PartitionsQ[#1], 2] == 1 & ]

Crossrefs

Cf. A000009, A000035, A000041, A001318, A001560, A280289, A280290, A280291.

Sequence in context: A278889 A075722 A169597 * A153712 A153711 A116049

Adjacent sequences: A280285 A280286 A280287 * A280289 A280290 A280291

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 31 2016

Status

approved