A280289 Numbers n such that number of partitions of n is odd and number of partitions of n into distinct parts is even.

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.

Links

Table of n, a(n) for n=1..75.

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

Index entries for related partition-counting sequences

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 & ]

Crossrefs

Cf. A000009, A000035, A000041, A052002, A090864, A280288, A280290, A280291.

Sequence in context: A009287 A061080 A254049 * A137027 A244409 A102733

Adjacent sequences: A280286 A280287 A280288 * A280290 A280291 A280292

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 31 2016

Status

approved