A235711 Arithmetic derivative of quarter squares.

0, 0, 0, 1, 4, 5, 6, 16, 32, 24, 10, 31, 60, 41, 14, 92, 192, 156, 108, 123, 140, 87, 22, 188, 384, 220, 26, 131, 252, 247, 240, 608, 1024, 560, 34, 375, 756, 417, 38, 476, 960, 704, 420, 493, 572, 321, 46, 1036, 2112, 1340, 500, 635, 780, 1107, 1458, 1620

Offset: 0

Author

Reinhard Zumkeller, Mar 18 2014

Keywords

• nonn
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002620, A003415, A068720.

Programs

Haskell

a235711 = a003415 . a002620

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[0] = ad[1] = 0; a[n_] := ad[Floor[n^2/4]]; Array[a, 100, 0] (* Amiram Eldar, Apr 11 2025 *)

Formula

a(n) = A003415(A002620(n));

a(2*n) = A068720(n), n > 0.