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Search: id:A113222
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| A113222 |
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a(n) = sum{p=primes, p|n} F(p^(m_{n,p})), where p^(m_{n,p}) is highest power of p dividing n, m= nonnegative integer and F(k) is the k-th Fibonacci number. |
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+0
3
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| 0, 1, 2, 3, 5, 3, 13, 21, 34, 6, 89, 5, 233, 14, 7, 987, 1597, 35, 4181, 8, 15, 90, 28657, 23, 75025, 234, 196418, 16, 514229, 8, 1346269, 2178309, 91, 1598, 18, 37, 24157817, 4182, 235, 26, 165580141, 16, 433494437, 92, 39, 28658, 2971215073, 989
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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Additive with a(p^e) = F(p^e).
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EXAMPLE
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12 = 2^2 * 3^1. So a(12) = F(2^2) + F(3^1) = 3 + 2 = 5.
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MATHEMATICA
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f[n_] := Plus @@ (Fibonacci[ #[[1]]^#[[2]]] & /@ FactorInteger[n]); Table[ f[n], {n, 49}] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A113195.
Sequence in context: A125677 A051358 A107473 this_sequence A060444 A152814 A021981
Adjacent sequences: A113219 A113220 A113221 this_sequence A113223 A113224 A113225
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Oct 18 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 21 2005
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