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A272440 Numbers n such that the average of the positive divisors of n is a Fibonacci number. 1
1, 3, 5, 6, 21, 41, 45, 65, 67, 68, 78, 96, 109, 382, 497, 517, 527, 658, 682, 705, 759, 805, 930, 966, 1155, 1557, 1973, 3211, 3653, 4563, 5167, 5620, 9037, 10027, 10117, 13279, 17353, 28856, 35174, 35534, 45459, 56072, 154555, 175151, 177721, 181561, 183181, 184201, 184421, 184601, 185466, 226666 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

1, 3, 5 and 21 are Fibonacci numbers. Are there other Fibonacci numbers in this sequence?

For a similar question and related proof attempt see the paper in the links section of A272412.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..734

EXAMPLE

3 is a term because 3 is divisible by 1 and 3. Average of 3 and 1 is 2 that is a Fibonacci number.

MATHEMATICA

s = Array[Fibonacci, {28}]; Select[Range@ Max@ s, MemberQ[s, Mean@ Divisors@ #] &] (* Michael De Vlieger, Apr 29 2016 *)

PROG

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

is(n)=my(f=factor(n), s=sigma(f), d=numdiv(f)); s%d==0 && isFibonacci(s/d) \\ Charles R Greathouse IV, May 02 2016

CROSSREFS

Cf. A000045, A003601, A272412.

Sequence in context: A282809 A168156 A295403 * A276704 A103022 A086189

Adjacent sequences:  A272437 A272438 A272439 * A272441 A272442 A272443

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Apr 29 2016

STATUS

approved

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Last modified August 17 22:59 EDT 2019. Contains 326059 sequences. (Running on oeis4.)