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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Mar 18 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

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

Cf. also A005086, A093653.

Programs

PARI

A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
A007895(n) = { my(s=0); while(n>0, s++; n -= fibonacci(1+A072649(n))); (s); };
A300837(n) = sumdiv(n,d,A007895(d));

Formula

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

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

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