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URL: https://oeis.org/A192016

⇱ A192016 - OEIS

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A192016
Second arithmetic derivative of prime powers: a(n) = A068346(A000961(n)).
3
0, 0, 0, 4, 0, 0, 16, 5, 0, 0, 80, 0, 0, 0, 7, 27, 0, 0, 176, 0, 0, 0, 0, 9, 0, 0, 0, 640, 0, 0, 0, 0, 216, 0, 0, 0, 0, 0, 0, 0, 0, 13, 55, 0, 1408, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 621, 0, 5120, 0, 0, 0, 0, 0, 0, 0, 19
OFFSET
1,4
LINKS
FORMULA
a(n) = A003415(A192015(n)).
a(A000040(n)) = 0; a(A002808(n)) > 0.
MATHEMATICA
ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; f[n_] := If[n == 1, 0, If[PrimePowerQ[n], {p, e} = FactorInteger[n][[1]]; e*p^(e-1), Nothing]]; ad /@ Array[f, 300] (* Amiram Eldar, Apr 11 2025 *)
PROG
(Haskell)
a192016 = a068346 . a000961 -- Reinhard Zumkeller, Apr 16 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 26 2011
STATUS
approved