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A280288
Numbers n such that number of partitions of n is even and number of partitions of n into distinct parts is odd.
3
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.
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 & ]
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 31 2016
STATUS
approved