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 A300837 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all divisors of n. 8

%I

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

%H Antti Karttunen, <a href="/A300837/b300837.txt">Table of n, a(n) for n = 1..10946</a>

%F a(n) = Sum_{d|n} A007895(d).

%F a(n) = A300836(n) + A007895(n).

%F For all n >=1, a(n) >= A005086(n).

%e 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 (PARI)

%o A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649

%o A007895(n) = { my(s=0); while(n>0, s++; n -= fibonacci(1+A072649(n))); (s); };

%o A300837(n) = sumdiv(n,d,A007895(d));

%Y Cf. A000045, A007895, A014417, A072649, A300835, A300836.

%Y Cf. also A005086, A093653.

%K nonn

%O 1,2

%A _Antti Karttunen_, Mar 18 2018

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Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)