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A300837 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all divisors of n.

%I A300837 #9 Mar 19 2018 22:15:34
%S A300837 1,2,2,4,2,5,3,5,4,5,3,10,2,6,5,7,4,9,4,10,5,6,3,13,5,5,7,11,3,13,4,
%T A300837 10,8,6,6,16,3,8,5,14,4,12,4,11,10,8,3,18,6,11,9,10,5,16,5,14,7,6,4,
%U A300837 23,4,8,9,13,6,16,5,10,7,14,4,23,4,8,12,12,8,13,4,20,10,9,5,23,9,9,8,17,2,22,6,12,8,6,8,24,3,12,13,19,5,15,4,14,13
%N A300837 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all divisors of n.
%H A300837 Antti Karttunen, <a href="/A300837/b300837.txt">Table of n, a(n) for n = 1..10946</a>
%F A300837 a(n) = Sum_{d|n} A007895(d).
%F A300837 a(n) = A300836(n) + A007895(n).
%F A300837 For all n >=1, a(n) >= A005086(n).
%e A300837 For n=12, its divisors are 1, 2, 3, 4, 6 and 12. Zeckendorf-representations (A014417) of these numbers are 1, 10, 100, 101, 1001 and 10101. Total number of 1's present is 10 (ten), thus a(12) = 10.
%o A300837 (PARI)
%o A300837 A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
%o A300837 A007895(n) = { my(s=0); while(n>0, s++; n -= fibonacci(1+A072649(n))); (s); };
%o A300837 A300837(n) = sumdiv(n,d,A007895(d));
%Y A300837 Cf. A000045, A007895, A014417, A072649, A300835, A300836.
%Y A300837 Cf. also A005086, A093653.
%K A300837 nonn
%O A300837 1,2
%A A300837 _Antti Karttunen_, Mar 18 2018