A157104 Arithmetic derivative of cubefree numbers.

0, 1, 1, 4, 1, 5, 1, 6, 7, 1, 16, 1, 9, 8, 1, 21, 1, 24, 10, 13, 1, 10, 15, 32, 1, 31, 1, 14, 19, 12, 60, 1, 21, 16, 1, 41, 1, 48, 39, 25, 1, 14, 45, 20, 56, 1, 16, 22, 31, 1, 92, 1, 33, 51, 18, 61, 1, 72, 26, 59, 1, 1, 39, 55, 80, 18, 71, 1, 43, 1, 124, 22, 45, 32, 1, 123, 20, 96, 34, 49

Offset: 1

Author

Reinhard Zumkeller, Feb 23 2009

Keywords

• nonn

Comments

a(n) = A003415(A004709(n)).

Links

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

Crossrefs

Cf. A068328, A068720.

Programs

Haskell

a157104 = a003415 . a004709  -- Reinhard Zumkeller, May 24 2013

Mathematica

Reap[Do[f = FactorInteger[n]; If[n == 1, Sow[0], If[And @@ (# <= 2 & ) /@ f[[All, 2]], Sow[Total[n*(f[[All, 2]]/f[[All, 1]])]]]], {n, 1, 100}]][[2, 1]] (* Jean-François Alcover, May 16 2013 *)