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
Keywords
Examples
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.
Programs
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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}] -
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
Comments