A293436 a(n) is the sum of the proper divisors of n that are Fibonacci numbers (A000045).

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10946

Index entries for sequences related to sums of divisors

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. A000045, A005092, A010056, A293435.

Cf. also A293434.

Sequence in context: A090049 A115364 A016476 * A293228 A169814 A068436

Adjacent sequences: A293433 A293434 A293435 * A293437 A293438 A293439

Keyword

nonn

Author

Antti Karttunen, Oct 09 2017

Status

approved