A068720 Arithmetic derivative of squares: a(n) = 2*n*A003415(n).

0, 4, 6, 32, 10, 60, 14, 192, 108, 140, 22, 384, 26, 252, 240, 1024, 34, 756, 38, 960, 420, 572, 46, 2112, 500, 780, 1458, 1792, 58, 1860, 62, 5120, 924, 1292, 840, 4320, 74, 1596, 1248, 5440, 82, 3444, 86, 4224, 3510, 2300, 94

Offset: 1

Author

Reinhard Zumkeller, Feb 26 2002

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A003415, A068719, A068721, A235711.

Programs

Haskell

a068720 = a003415 . a000290  -- Reinhard Zumkeller, Mar 18 2014

Magma

Ad:=func; [0] cat [Ad(n^2): n in [2..50]]; // Bruno Berselli, Oct 22 2013

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; a[n_] := 2 * n * ad[n]; Array[a, 100] (* Amiram Eldar, Apr 11 2025 *)

Formula

a(n) = A003415(n^2) = 2*n*A003415(n).

a(n) = A235711(2*n). - Reinhard Zumkeller, Mar 18 2014