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A068327 Arithmetic derivative of n^n. 6
0, 0, 4, 27, 1024, 3125, 233280, 823543, 201326592, 2324522934, 70000000000, 285311670611, 142657607172096, 302875106592253, 100008061430022144, 3503151123046875000, 590295810358705651712, 827240261886336764177, 826274569581227289083904 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

p prime: a(p) = A003415(p^p)) = p^p,

A003415(A051674(n)) = A051674(n).

LINKS

T. D. Noe and Alois P. Heinz, Table of n, a(n) for n = 0..380 (first 100 terms from T. D. Noe)

FORMULA

a(n) = A003415(A000312(n)).

a(n) = n^n * A003415(n) = A000312(n) * A003415(n). - Alois P. Heinz, Jun 09 2015

EXAMPLE

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.

MAPLE

a:= n-> n^(n+1)*add(i[2]/i[1], i=ifactors(n)[2]):

seq(a(n), n=0..30);  # Alois P. Heinz, Jun 09 2015

MATHEMATICA

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-Fran├žois Alcover, Mar 27 2013 *)

CROSSREFS

Cf. A000312, A003415.

Sequence in context: A210343 A104168 A197990 * A066842 A133032 A271385

Adjacent sequences:  A068324 A068325 A068326 * A068328 A068329 A068330

KEYWORD

nonn,nice

AUTHOR

Reinhard Zumkeller, Feb 27 2002

STATUS

approved

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Last modified October 23 12:10 EDT 2018. Contains 316527 sequences. (Running on oeis4.)