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A272412 Numbers n such that sigma(n) is a Fibonacci number. 11

%I #47 Jun 17 2021 05:18:31

%S 1,2,7,9,66,70,94,115,119,2479,18084,19180,19290,22060,23156,23178,

%T 24934,24956,25756,26715,27034,28678,28965,29578,30094,32253,32793,

%U 34113,35365,38635,39319,40963,42493,44413,45223,45653,322032,429424,503175,624027,670975

%N Numbers n such that sigma(n) is a Fibonacci number.

%C 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).

%C 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.

%H Charles R Greathouse IV, <a href="/A272412/b272412.txt">Table of n, a(n) for n = 1..10000</a>

%H Max Alekseyev, <a href="http://home.gwu.edu/~maxal/gpscripts/">PARI/GP Scripts for Miscellaneous Math Problems</a>

%H Sergei V. Konyagin, Florian Luca and Pantelimon Stanica, <a href="https://math.boku.ac.at/udt/vol04/no1/KLS09-1.pdf">Sum Of Divisors Of Fibonacci Numbers</a>, Uniform Distribution Theory 4 (2009), no.1, 1-8.

%H N. J. A. Sloane, <a href="/A272412/a272412.pdf">The OEIS, Mathematical Discovery, and Insomnia</a>, Slides of plenary talk presented at Computational Discovery in Mathematics, Western University, London, Ontario, May 12-16. Mentions this sequence at page 32.

%t f = Fibonacci@Range[2,40]; Select[Range[10^6], MemberQ[f, DivisorSigma[1, #]] &] (* _Giovanni Resta_, Apr 29 2016 *)

%o (PARI) lista(nn) = for(n=1, nn, if(issquare(5*sigma(n)^2+4) || issquare(5*sigma(n)^2-4), print1(n, ", ")));

%o (PARI) isFibonacci(n)=my(k=n^2);issquare(k+=(k+1)<<2) || (n>0 && issquare(k-8))

%o is(n)=isFibonacci(sigma(n)) \\ _Charles R Greathouse IV_, Apr 29 2016

%Y Cf. A000045, A000203.

%K nonn,look

%O 1,2

%A _Altug Alkan_, Apr 29 2016

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Last modified March 29 06:34 EDT 2024. Contains 371265 sequences. (Running on oeis4.)