|
%I #12 Apr 14 2021 22:25:55
%S 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,
%T 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,
%U 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
%N a(n) is the sum of the proper divisors of n that are Fibonacci numbers (A000045).
%H Antti Karttunen, <a href="/A293436/b293436.txt">Table of n, a(n) for n = 1..10946</a>
%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>
%F a(n) = Sum_{d|n, d<n} A010056(d)*d.
%F a(n) = A005092(n) - (A010056(n)*n).
%F G.f.: Sum_{k>=2} Fibonacci(k) * x^(2*Fibonacci(k)) / (1 - x^Fibonacci(k)). - _Ilya Gutkovskiy_, Apr 14 2021
%e 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.
%e 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.
%t With[{s = Fibonacci@ Range[2, 40]}, Table[DivisorSum[n, # &, And[MemberQ[s, #], # != n] &], {n, 105}]] (* _Michael De Vlieger_, Oct 09 2017 *)
%o (PARI)
%o 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
%o A293436(n) = sumdiv(n,d,(d<n)*A010056(d)*d);
%Y Cf. A000045, A005092, A010056, A293435.
%Y Cf. also A293434.
%K nonn
%O 1,4
%A _Antti Karttunen_, Oct 09 2017
|
