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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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A224323 A240650 A011804 * A291622 A058156 A011837 Adjacent sequences:  A292464 A292465 A292466 * A292468 A292469 A292470 KEYWORD nonn AUTHOR Michel Lagneau, Sep 22 2017 STATUS approved

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Last modified August 23 22:45 EDT 2019. Contains 326254 sequences. (Running on oeis4.)