A113177 If, for p prime, p^(m_{n,p}) is the highest power of p dividing n with m>=0, then a(n) = Sum_{p prime} F(p)*(m_{n,p}), where F(p) = p-th Fibonacci number.

0, 1, 2, 2, 5, 3, 13, 3, 4, 6, 89, 4, 233, 14, 7, 4, 1597, 5, 4181, 7, 15, 90, 28657, 5, 10, 234, 6, 15, 514229, 8, 1346269, 5, 91, 1598, 18, 6, 24157817, 4182, 235, 8, 165580141, 16, 433494437, 91, 9, 28658, 2971215073, 6, 26, 11, 1599, 235, 53316291173, 7, 94

Offset

1,3

Links

Danny Rorabaugh, Table of n, a(n) for n = 1..4000

Formula

Totally additive with a(p) = F(p).

Example

12 = 2^2 * 3^1, so a(12) = F(2)*2 + F(3)*1 = 2 + 2 = 4.

Mathematica

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

Prog

(PARI) { for(n=1, 100, f=factor(n); s=0; for(i=1, matsize(f)[1], s+=fibonacci(f[i, 1])*f[i, 2]); print1(s, ", ")) } \\ Lambert Klasen, Oct 26 2005
(Sage) [0]+[sum([fibonacci(x[0])*x[1] for x in factor(n)]) for n in range(2, 56)] # Danny Rorabaugh, Apr 03 2015

Crossrefs

Cf. A113178, A000045.

Sequence in context: A241820 A190170 A147524 * A344507 A322786 A184243

Adjacent sequences: A113174 A113175 A113176 * A113178 A113179 A113180

Keyword

nonn,easy

Author

Leroy Quet, Oct 16 2005

Extensions

More terms from Esa Peuha (esa.peuha(AT)helsinki.fi) and Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 26 2005

Status

approved