A292467 Smallest integer such that the sum of its n smallest divisors is a Fibonacci number, or 0 if no such integer exists.

1, 2, 9, 94, 18, 60, 210, 36, 510, 624, 90, 4290, 2604, 2340, 792, 8512, 9324, 3960, 9396, 600, 3600, 7840, 5472, 6840, 5520, 10296, 7800, 6120, 12768, 9450, 18240, 33600, 16200, 37800, 27360, 68796, 222768, 59400, 118944, 156240, 139320, 99360, 302400, 288512

Offset

1,2

Comments

The first corresponding Fibonacci numbers are 1, 3, 13, 144, 21, 21, 34, 55, 89, 89, 144, 144, 233, 144, 233, ...

The first squares of the sequence are 1, 9, 36, 3600, ...

Links

Table of n, a(n) for n=1..44.

Example

a(5)=18 because the sum of the 5 smallest divisors of 18, i.e., 1 + 2 + 3 + 6 + 9 = 21, is a Fibonacci number.

Mathematica

Table[k=1; While[Nand[Length@#>=n, IntegerQ[Sqrt[5*Total@Take[PadRight[#, n], n]^2-4]]||IntegerQ[Sqrt[5*Total@Take[PadRight[#, n], n]^2+4]]]&@Divisors@k, k++]; k, {n, 1, 45}]

Prog

(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)) ;
a(n) = {my(k = 1); while((d=divisors(k)) && !((#d >= n) && isfib(sum(i=1, n, d[i]))), k++); k; } \\ Michel Marcus, Oct 01 2017

Crossrefs

Cf. A000045, A240698, A289712, A289776.

Sequence in context: A356566 A365363 A011804 * A291622 A058156 A381984

Adjacent sequences: A292464 A292465 A292466 * A292468 A292469 A292470

Keyword

nonn

Author

Michel Lagneau, Sep 22 2017

Status

approved