|
%I #12 Mar 19 2018 22:15:27
%S 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,
%T 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,
%U 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
%N a(n) is the total number of terms (1-digits) in Zeckendorf representation of all proper divisors of n.
%H Antti Karttunen, <a href="/A300836/b300836.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = Sum_{d|n, d<n} A007895(d).
%F a(n) = A300837(n) - A007895(n).
%F a(n) = A001222(A300834(n)).
%F For all n >=1, a(n) >= A293435(n).
%e 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.
%o (PARI)
%o A072649(n) = { my(m); if(n<1, 0, m=0; until(fibonacci(m)>n, m++); m-2); }; \\ From A072649
%o A007895(n) = { my(s=0); while(n>0, s++; n -= fibonacci(1+A072649(n))); (s); }
%o A300836(n) = sumdiv(n,d,(d<n)*A007895(d));
%Y Cf. A000045, A007895, A014417, A072649, A300834, A300837.
%Y Cf. also A292257, A293435.
%K nonn
%O 1,4
%A _Antti Karttunen_, Mar 18 2018
|
