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A272412 Numbers n such that sigma(n) is a Fibonacci number. 8
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 September 20 01:52 EDT 2019. Contains 327207 sequences. (Running on oeis4.)