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

1,2

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 A362858

Adjacent sequences: A272409 A272410 A272411 * A272413 A272414 A272415

Keyword

nonn,look

Author

Altug Alkan, Apr 29 2016

Status

approved