A280291 Numbers n such that number of partitions of n is odd and number of partitions of n into distinct parts is odd.

0, 1, 5, 7, 12, 35, 51, 77, 92, 145, 155, 210, 222, 287, 301, 330, 345, 376, 392, 425, 442, 477, 495, 610, 672, 737, 805, 852, 876, 1190, 1247, 1335, 1426, 1617, 1717, 1855, 1962, 2035, 2147, 2542, 2625, 2795, 2882, 3197, 3337, 3480, 3626, 3775, 3876, 4030, 4347, 4510, 4565, 4845, 4902

Offset

1,3

Comments

Intersection of A001318 and A052002.

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

Links

Table of n, a(n) for n=1..55.

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

Index entries for related partition-counting sequences

Example

7 is in the sequence because we have:
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number of partitions = 15 (is odd)
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7 = 7
6 + 1 = 7
5 + 2 = 7
5 + 1 + 1 = 7
4 + 3 = 7
4 + 2 + 1 = 7
4 + 1 + 1 + 1 = 7
3 + 3 + 1 = 7
3 + 2 + 2 = 7
3 + 2 + 1 + 1 = 7
3 + 1 + 1 + 1 + 1 = 7
2 + 2 + 2 + 1 = 7
2 + 2 + 1 + 1 + 1 = 7
2 + 1 + 1 + 1 + 1 + 1 = 7
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
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number of partitions into distinct parts = 5 (is odd)
-----------------------------------------------------
7 = 7
6 + 1 = 7
5 + 2 = 7
4 + 3 = 7
4 + 2 + 1 = 7

Mathematica

Join[{0}, Select[Range[5000], Mod[PartitionsP[#1], 2] == Mod[PartitionsQ[#1], 2] == 1 & ]]

Crossrefs

Cf. A000009, A000035, A000041, A001318, A052002, A280288, A280289, A280290.

Sequence in context: A247027 A020686 A011984 * A195557 A063187 A335164

Adjacent sequences: A280288 A280289 A280290 * A280292 A280293 A280294

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Dec 31 2016

Extensions

a(1)=0 inserted by Alois P. Heinz, Dec 31 2016

Status

approved