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A113178 a(n) = Sum_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the sum is over the distinct prime divisors of n. 2

%I #22 Jan 02 2024 00:13:12

%S 0,1,2,1,5,3,13,1,2,6,89,3,233,14,7,1,1597,3,4181,6,15,90,28657,3,5,

%T 234,2,14,514229,8,1346269,1,91,1598,18,3,24157817,4182,235,6,

%U 165580141,16,433494437,90,7,28658,2971215073,3,13,6,1599,234

%N a(n) = Sum_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the sum is over the distinct prime divisors of n.

%H Danny Rorabaugh, <a href="/A113178/b113178.txt">Table of n, a(n) for n = 1..4000</a>

%F Additive with a(p^e) = F(p).

%e 12 = 2^2 * 3^1, so a(12) = F(2) + F(3) = 1 + 2 = 3.

%t b[t_]:=Fibonacci[First[t]] a[n_]:=Apply[Plus, Map[b, FactorInteger[n]]] (* Esa Peuha, Oct 26 2005 *)

%o (Sage) [0]+[sum([fibonacci(p) for p in prime_factors(n)]) for n in range(2,53)] # _Danny Rorabaugh_, Apr 03 2015

%Y Cf. A000045, A113177.

%K nonn,easy

%O 1,3

%A _Leroy Quet_, Oct 16 2005

%E More terms from Esa Peuha (esa.peuha(AT)helsinki.fi), Oct 26 2005

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Last modified February 29 19:20 EST 2024. Contains 370428 sequences. (Running on oeis4.)