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A300837 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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 A125296 A294097

Adjacent sequences:  A300834 A300835 A300836 * A300838 A300839 A300840

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 18 2018

STATUS

approved

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Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)