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A113177
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If, for p = prime, p^(m_{n,p}) is highest power of p dividing n, m= nonnegative integer, then a(n) is sum over all primes of F(p)*(m_{n,p}), where F(p)= pth Fibonacci number.
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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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FORMULA
| Totally additive with a(p) = F(p).
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EXAMPLE
| 12 = 2^2 * 3^1, so a(12) = F(2)*2 + F(3)*1 = 2 + 2 = 4.
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MATHEMATICA
| b[t_]:=Fibonacci[First[t]]Last[t] a[n_]:=Apply[Plus, Map[b, FactorInteger[n]]] (Peuha)
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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, ", ")) } (Klasen)
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CROSSREFS
| Cf. A113178, A000045.
Sequence in context: A006800 A190170 A147524 * A184243 A135281 A068465
Adjacent sequences: A113174 A113175 A113176 * A113178 A113179 A113180
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Oct 16 2005
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EXTENSIONS
| More terms from Esa Peuha (esa.peuha(AT)helsinki.fi) and Lambert Klasen (lambert.klasen(AT)gmx.net), Oct 26 2005
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