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A339461
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Number of Fibonacci divisors of n^2 + 1.
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6
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1, 2, 2, 3, 1, 3, 1, 3, 3, 2, 1, 2, 2, 4, 1, 2, 1, 3, 3, 2, 1, 4, 2, 3, 1, 2, 1, 3, 2, 2, 1, 3, 2, 3, 3, 2, 1, 3, 2, 2, 1, 2, 2, 3, 2, 2, 1, 5, 2, 2, 1, 2, 2, 3, 1, 4, 1, 4, 2, 2, 2, 2, 2, 3, 1, 2, 1, 3, 2, 2, 3, 2, 2, 4, 1, 2, 1, 3, 2, 2, 1, 3, 2, 4, 1, 2, 2
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OFFSET
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0,2
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LINKS
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FORMULA
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EXAMPLE
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a(13) = 4 because the divisors of 13^2 + 1 = 170 are {1, 2, 5, 10, 17, 34, 85, 170} with 4 Fibonacci divisors: 1, 2, 5 and 34.
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MAPLE
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with(numtheory):with(combinat, fibonacci):nn:=100:F:={}:
for k from 1 to nn do:
F:=F union {fibonacci(k)}:
od:
for n from 0 to 90 do:
f:=n^2+1:d:=divisors(f):
lst:= F intersect d: n1:=nops(lst):printf(`%d, `, n1):
od:
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MATHEMATICA
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Array[DivisorSum[#^2 + 1, 1 &, Or @@ Map[IntegerQ@ Sqrt[#] &, 5 #^2 + 4 {-1, 1}] &] &, 105, 0] (* Michael De Vlieger, Dec 07 2020 *)
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PROG
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(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8);
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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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