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 A272412 Numbers n such that sigma(n) is a Fibonacci number. 11
 1, 2, 7, 9, 66, 70, 94, 115, 119, 2479, 18084, 19180, 19290, 22060, 23156, 23178, 24934, 24956, 25756, 26715, 27034, 28678, 28965, 29578, 30094, 32253, 32793, 34113, 35365, 38635, 39319, 40963, 42493, 44413, 45223, 45653, 322032, 429424, 503175, 624027, 670975 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Konyagin, Luca & Stanica proved that for almost all positive integers n, the sum of the divisors of Fibonacci(n) is not a Fibonacci number (see page 7). If the sum of the k-th powers of the divisors of Fibonacci(n) is a Fibonacci number for k > 1, then the corresponding Fibonacci(n) is 1 or 2. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 Max Alekseyev, PARI/GP Scripts for Miscellaneous Math Problems Sergei V. Konyagin, Florian Luca and Pantelimon Stanica, Sum Of Divisors Of Fibonacci Numbers, Uniform Distribution Theory 4 (2009), no.1, 1-8. N. J. A. Sloane, The OEIS, Mathematical Discovery, and Insomnia, Slides of plenary talk presented at Computational Discovery in Mathematics, Western University, London, Ontario, May 12-16. Mentions this sequence at page 32. MATHEMATICA f = Fibonacci@Range[2, 40]; Select[Range[10^6], MemberQ[f, DivisorSigma[1, #]] &] (* Giovanni Resta, Apr 29 2016 *) PROG (PARI) lista(nn) = for(n=1, nn, if(issquare(5*sigma(n)^2+4) || issquare(5*sigma(n)^2-4), print1(n, ", "))); (PARI) isFibonacci(n)=my(k=n^2); issquare(k+=(k+1)<<2) || (n>0 && issquare(k-8)) is(n)=isFibonacci(sigma(n)) \\ Charles R Greathouse IV, Apr 29 2016 CROSSREFS Cf. A000045, A000203. Sequence in context: A002353 A041073 A079942 * A042561 A252661 A041453 Adjacent sequences:  A272409 A272410 A272411 * A272413 A272414 A272415 KEYWORD nonn,look AUTHOR Altug Alkan, Apr 29 2016 STATUS approved

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Last modified August 10 06:08 EDT 2022. Contains 356029 sequences. (Running on oeis4.)