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A068327
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Arithmetic derivative of n^n.
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5
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0, 4, 27, 1024, 3125, 233280, 823543, 201326592, 2324522934, 70000000000, 285311670611, 142657607172096, 302875106592253, 100008061430022144, 3503151123046875000, 590295810358705651712
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OFFSET
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1,2
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COMMENTS
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p prime: a(p) = A003415(p^p)) = p^p,
A003415(A051674(n))=A051674(n).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
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FORMULA
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a(n) = A003415(A000312(n)).
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EXAMPLE
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a(10) = A003415(10^10) = A003415(2^10 * 5^10) = 10^10 * (10/2 + 10/5) = 10^10 * (5 + 2) = 70000000000 by formula in A003415.
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MATHEMATICA
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a312[n_] := Sum[ StirlingS2[n, k]*n!/(n - k)!, {k, 0, n}]; a3415[n_] := With[ {fi = FactorInteger[n]}, n*Total[ fi[[All, 2]] / fi[[All, 1]] ] ]; a3415[0] = a3415[1] = 0; a[n_] := a3415[ a312[n] ]; Table[ a[n], {n, 1, 16}] (* Jean-François Alcover, Mar 27 2013 *)
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CROSSREFS
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Sequence in context: A210343 A104168 A197990 * A066842 A133032 A110763
Adjacent sequences: A068324 A068325 A068326 * A068328 A068329 A068330
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KEYWORD
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nonn,nice
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AUTHOR
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Reinhard Zumkeller, Feb 27 2002
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STATUS
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approved
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