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A258565
Arithmetic derivative of powerful numbers, cf. A001694.
1
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
1,2
LINKS
FORMULA
a(n) = A003415(A001694(n)).
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 *)
PROG
(Haskell)
a258565 = a003415 . a001694
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 03 2015
STATUS
approved