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A292467
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Smallest integer such that the sum of its n smallest divisors is a Fibonacci number, or 0 if no such integer exists.
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0
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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
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OFFSET
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1,2
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COMMENTS
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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, ...
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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