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A272412
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Numbers n such that sigma(n) is a Fibonacci number.
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8
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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
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internal format)
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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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.
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MATHEMATICA
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f = Fibonacci@Range[2, 40]; Select[Range[10^6], MemberQ[f, DivisorSigma[1, #]] &] (* Giovanni Resta, Apr 29 2016 *)
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PROG
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(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
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CROSSREFS
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Cf. A000045, A000203.
Sequence in context: A002353 A041073 A079942 * A042561 A252661 A041453
Adjacent sequences: A272409 A272410 A272411 * A272413 A272414 A272415
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KEYWORD
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nonn,look
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AUTHOR
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Altug Alkan, Apr 29 2016
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STATUS
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approved
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