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

Author

Ilya Gutkovskiy, Dec 31 2016

Keywords

• nonn
• easy

Comments

Intersection of A001318 and A052002.

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

Examples

			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)
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7 = 7
6 + 1 = 7
5 + 2 = 7
4 + 3 = 7
4 + 2 + 1 = 7
		

Links

• Eric Weisstein's World of Mathematics, Partition Function P, Partition Function Q
• Index entries for related partition-counting sequences

Crossrefs

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

Programs

Mathematica

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

Extensions

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