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A339461 Number of Fibonacci divisors of n^2 + 1. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(A005574(n)) = 1 for n > 2.
a(n) = A005086(A002522(n)). - Michel Marcus, Dec 06 2020
EXAMPLE
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.
MAPLE
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:
MATHEMATICA
Array[DivisorSum[#^2 + 1, 1 &, Or @@ Map[IntegerQ@ Sqrt[#] &, 5 #^2 + 4 {-1, 1}] &] &, 105, 0] (* Michael De Vlieger, Dec 07 2020 *)
PROG
(PARI) isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || issquare(k-8);
a(n) = sumdiv(n^2+1, d, isfib(d)); \\ Michel Marcus, Dec 06 2020
CROSSREFS
Sequence in context: A265576 A083040 A083899 * A190263 A144911 A233431
KEYWORD
nonn
AUTHOR
Michel Lagneau, Dec 06 2020
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)