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

1,2

Links

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

Formula

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

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

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

Example

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.

Prog

(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));

Crossrefs

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

Cf. also A005086, A093653.

Sequence in context: A005128 A187782 A129296 * A321443 A333836 A125296

Adjacent sequences: A300834 A300835 A300836 * A300838 A300839 A300840

Keyword

nonn

Author

Antti Karttunen, Mar 18 2018

Status

approved