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A293436
a(n) is the sum of the proper divisors of n that are Fibonacci numbers (A000045).
3
0, 1, 1, 3, 1, 6, 1, 3, 4, 8, 1, 6, 1, 3, 9, 11, 1, 6, 1, 8, 4, 3, 1, 14, 6, 16, 4, 3, 1, 11, 1, 11, 4, 3, 6, 6, 1, 3, 17, 16, 1, 27, 1, 3, 9, 3, 1, 14, 1, 8, 4, 16, 1, 6, 6, 11, 4, 3, 1, 11, 1, 3, 25, 11, 19, 6, 1, 37, 4, 8, 1, 14, 1, 3, 9, 3, 1, 19, 1, 16, 4, 3, 1, 27, 6, 3, 4, 11, 1, 11, 14, 3, 4, 3, 6, 14, 1, 3, 4, 8, 1, 40, 1, 24, 30
OFFSET
1,4
FORMULA
a(n) = Sum_{d|n, d<n} A010056(d)*d.
a(n) = A005092(n) - (A010056(n)*n).
G.f.: Sum_{k>=2} Fibonacci(k) * x^(2*Fibonacci(k)) / (1 - x^Fibonacci(k)). - Ilya Gutkovskiy, Apr 14 2021
EXAMPLE
For n = 55, its proper divisors are [1, 5, 11], of which only 1 and 5 are in A000045, thus a(55) = 1 + 5 = 6.
For n = 10946, its proper divisors are [1, 2, 13, 26, 421, 842, 5473], and only 1, 2 and 13 are Fibonacci numbers, thus a(10946) = 1 + 2 + 13 = 16.
MATHEMATICA
With[{s = Fibonacci@ Range[2, 40]}, Table[DivisorSum[n, # &, And[MemberQ[s, #], # != n] &], {n, 105}]] (* Michael De Vlieger, Oct 09 2017 *)
PROG
(PARI)
A010056(n) = { my(k=n^2); k+=(k+1)<<2; (issquare(k) || (n>0 && issquare(k-8))) }; \\ This function from Charles R Greathouse IV, Jul 30 2012
A293436(n) = sumdiv(n, d, (d<n)*A010056(d)*d);
CROSSREFS
Cf. also A293434.
Sequence in context: A090049 A115364 A016476 * A293228 A169814 A068436
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 09 2017
STATUS
approved