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A300836 a(n) is the total number of terms (1-digits) in Zeckendorf representation of all proper divisors of n. 8
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 (list; graph; refs; listen; history; text; internal format)
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: A292587 A097283 A296119 * A118314 A002033 A074206

Adjacent sequences:  A300833 A300834 A300835 * A300837 A300838 A300839

KEYWORD

nonn

AUTHOR

Antti Karttunen, Mar 18 2018

STATUS

approved

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Last modified October 17 08:36 EDT 2019. Contains 328107 sequences. (Running on oeis4.)