A300836 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all proper divisors of n.

0, 1, 1, 2, 1, 3, 1, 4, 2, 3, 1, 7, 1, 4, 3, 5, 1, 7, 1, 7, 4, 4, 1, 11, 2, 3, 4, 8, 1, 10, 1, 7, 4, 5, 4, 14, 1, 5, 3, 11, 1, 10, 1, 8, 7, 4, 1, 15, 3, 8, 5, 7, 1, 12, 4, 12, 5, 4, 1, 21, 1, 5, 7, 10, 3, 13, 1, 8, 4, 11, 1, 19, 1, 4, 8, 10, 5, 10, 1, 16, 7, 5, 1, 20, 5, 5, 4, 12, 1, 20, 4, 10, 5, 4, 5, 21, 1, 9, 10, 16, 1, 13, 1, 11, 10

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

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

a(n) = A300837(n) - A007895(n).

a(n) = A001222(A300834(n)).

For all n >=1, a(n) >= A293435(n).

Example

For n=12, its proper divisors are 1, 2, 3, 4 and 6. Zeckendorf-representations (A014417) of these numbers are 1, 10, 100, 101 and 1001. Total number of 1's present is 7, thus a(12) = 7.

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); }
A300836(n) = sumdiv(n, d, (d<n)*A007895(d));

Crossrefs

Cf. A000045, A007895, A014417, A072649, A300834, A300837.

Cf. also A292257, A293435.

Sequence in context: A334033 A339564 A296119 * A118314 A349059 A002033

Adjacent sequences: A300833 A300834 A300835 * A300837 A300838 A300839

Keyword

nonn

Author

Antti Karttunen, Mar 18 2018

Status

approved