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

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

Offset: 1

Author

Altug Alkan, Apr 29 2016

Keywords

• nonn
• look

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.

Crossrefs

Cf. A000045, A000203.

Programs

Mathematica

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

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