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

%I A292467 #35 Oct 31 2017 16:28:28
%S A292467 1,2,9,94,18,60,210,36,510,624,90,4290,2604,2340,792,8512,9324,3960,
%T A292467 9396,600,3600,7840,5472,6840,5520,10296,7800,6120,12768,9450,18240,
%U A292467 33600,16200,37800,27360,68796,222768,59400,118944,156240,139320,99360,302400,288512
%N A292467 Smallest integer such that the sum of its n smallest divisors is a Fibonacci number, or 0 if no such integer exists.
%C A292467 The first corresponding Fibonacci numbers are 1, 3, 13, 144, 21, 21, 34, 55, 89, 89, 144, 144, 233, 144, 233, ...
%C A292467 The first squares of the sequence are 1, 9, 36, 3600, ...
%e A292467 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 A292467 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 A292467 (PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8)) ;
%o A292467 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 A292467 Cf. A000045, A240698, A289712, A289776.
%K A292467 nonn
%O A292467 1,2
%A A292467 _Michel Lagneau_, Sep 22 2017