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

1,2

Links

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

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

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

Sequence in context: A336862 A190392 A133517 * A335914 A331054 A361192

Adjacent sequences: A258562 A258563 A258564 * A258566 A258567 A258568

Keyword

nonn

Author

Reinhard Zumkeller, Jun 03 2015

Status

approved