A292467 - OEIS

%I #35 Oct 31 2017 16:28:28

%S 1,2,9,94,18,60,210,36,510,624,90,4290,2604,2340,792,8512,9324,3960,

%T 9396,600,3600,7840,5472,6840,5520,10296,7800,6120,12768,9450,18240,

%U 33600,16200,37800,27360,68796,222768,59400,118944,156240,139320,99360,302400,288512

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

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

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

%e 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.

%t 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}]

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

%o 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

%Y Cf. A000045, A240698, A289712, A289776.

%K nonn

%O 1,2

%A _Michel Lagneau_, Sep 22 2017