A258565 Arithmetic derivative of powerful numbers, cf. A001694.

0, 4, 12, 6, 32, 10, 27, 80, 60, 14, 192, 156, 108, 140, 216, 22, 75, 448, 384, 26, 252, 380, 540, 240, 405, 1024, 912, 34, 756, 147, 38, 700, 960, 1296, 420, 572, 800, 2304, 46, 2112, 500, 1836, 945, 780, 1458, 1792, 2320, 58, 3024, 1860, 62, 1628, 2592

Offset: 1

Author

Reinhard Zumkeller, Jun 03 2015

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003415, A001694, A068720, A068328, A078310.

Programs

Haskell

a258565 = a003415 . a001694

Mathematica

ader[n_] := Switch[n, 0|1, 0, _, If[PrimeQ[n], 1, Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
ader /@ Join[{1}, Select[Range[1000], AllTrue[FactorInteger[#][[All, 2]], # > 1&]&]] (* Jean-François Alcover, Oct 12 2021 *)

Formula

a(n) = A003415(A001694(n)).