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 A270470 Integers n such that A001654(n) is divisible by n*(n+1)/2. 0
 1, 3, 10, 23, 24, 47, 60, 107, 108, 167, 180, 240, 250, 323, 383, 503, 540, 575, 600, 647, 660, 683, 768, 863, 1008, 1103, 1200, 1223, 1320, 1367, 1620, 1728, 1800, 1860, 2160, 2207, 2447, 2520, 2687, 2688, 2736, 3000, 3023, 3060, 3300, 3360, 3527, 3528, 3744, 3863, 3888, 4200, 4703, 4800 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Odd terms of this sequence are prime most of the time. Odd composite terms of this sequence are 1, 323, 575, 6479, 7055, ... LINKS EXAMPLE 3 is a term because (1^2 + 1^2 + 2^2) / (1 + 2 + 3) = 1. 10 is a term because (1^2 + 1^2 + 2^2 + 3^2 + 5^2 + 8^2 + 13^2 + 21^2 + 34^2 + 55^2) / (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) = 89. MATHEMATICA nn = 4800; Function[k, Select[Range@ nn, Divisible[k[[# + 1]], # (# + 1)/2] &]]@ LinearRecurrence[{2, 2, -1}, {0, 1, 2}, nn + 1] (* Michael De Vlieger, Mar 19 2016, after Vladimir Joseph Stephan Orlovsky at A001654 *) PROG (PARI) a(n) = fibonacci(n)*fibonacci(n+1); for(n=1, 1e4, if(a(n) % (n*(n+1)/2) ==0, print1(n, ", "))); CROSSREFS Cf. A000217, A001654. Sequence in context: A171686 A027164 A292921 * A166119 A041403 A077126 Adjacent sequences: A270467 A270468 A270469 * A270471 A270472 A270473 KEYWORD nonn AUTHOR Altug Alkan, Mar 17 2016 STATUS approved

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Last modified February 2 04:20 EST 2023. Contains 359997 sequences. (Running on oeis4.)