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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Intersection of A001318 and A001560. Numbers n such that A000035(A000041(n)) = 0 and A000035(A000009(n)) = 1. LINKS Table of n, a(n) for n=1..58. Eric Weisstein's World of Mathematics, Partition Function P, Partition Function Q Index entries for related partition-counting sequences EXAMPLE 15 is in the sequence because we have: ------------------------------------ number of partitions = 176 (is even) ------------------------------------ 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 ... ------------------------------------------------------ number of partitions into distinct parts = 27 (is odd) ------------------------------------------------------ 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 & ] CROSSREFS Cf. A000009, A000035, A000041, A001318, A001560, A280289, A280290, A280291. Sequence in context: A278889 A075722 A169597 * A153712 A153711 A116049 Adjacent sequences: A280285 A280286 A280287 * A280289 A280290 A280291 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Dec 31 2016 STATUS approved

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Last modified September 21 08:25 EDT 2023. Contains 365499 sequences. (Running on oeis4.)