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A280289
Numbers n such that number of partitions of n is odd and number of partitions of n into distinct parts is even.
3
3, 4, 6, 13, 14, 16, 17, 18, 20, 23, 24, 29, 32, 33, 36, 37, 38, 39, 41, 43, 44, 48, 49, 52, 53, 54, 56, 60, 61, 63, 67, 68, 69, 71, 72, 73, 76, 81, 82, 83, 85, 87, 88, 89, 90, 91, 93, 95, 99, 102, 104, 105, 107, 111, 114, 115, 118, 119, 121, 123, 127, 132, 134, 138, 139, 140, 143, 144, 146, 148, 150, 152, 156, 157, 159
OFFSET
1,1
COMMENTS
Intersection of A052002 and A090864.
Numbers n such that A000035(A000041(n)) = 1 and A000035(A000009(n)) = 0.
EXAMPLE
6 is in the sequence because we have:
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number of partitions = 11 (is odd)
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6 = 6
5 + 1 = 6
4 + 2 = 6
4 + 1 + 1 = 6
3 + 3 = 6
3 + 2 + 1 = 6
3 + 1 + 1 + 1 = 6
2 + 2 + 2 = 6
2 + 2 + 1 + 1 = 6
2 + 1 + 1 + 1 + 1 = 6
1 + 1 + 1 + 1 + 1 + 1 = 6
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number of partitions into distinct parts = 4 (is even)
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6 = 6
5 + 1 = 6
4 + 2 = 6
3 + 2 + 1 = 6
MATHEMATICA
Select[Range[160], Mod[PartitionsP[#1], 2] == 1 && Mod[PartitionsQ[#1], 2] == 0 & ]
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Dec 31 2016
STATUS
approved