cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A068720 #15 Apr 11 2025 03:32:03
%S A068720 0,4,6,32,10,60,14,192,108,140,22,384,26,252,240,1024,34,756,38,960,
%T A068720 420,572,46,2112,500,780,1458,1792,58,1860,62,5120,924,1292,840,4320,
%U A068720 74,1596,1248,5440,82,3444,86,4224,3510,2300,94
%N A068720 Arithmetic derivative of squares: a(n) = 2*n*A003415(n).
%H A068720 Bruno Berselli, <a href="/A068720/b068720.txt">Table of n, a(n) for n = 1..1000</a>
%F A068720 a(n) = A003415(n^2) = 2*n*A003415(n).
%F A068720 a(n) = A235711(2*n). - _Reinhard Zumkeller_, Mar 18 2014
%t A068720 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 *)
%o A068720 (Magma) Ad:=func<h | h*(&+[Factorisation(h)[i][2]/Factorisation(h)[i][1]: i in [1..#Factorisation(h)]])>; [0] cat [Ad(n^2): n in [2..50]]; // _Bruno Berselli_, Oct 22 2013
%o A068720 (Haskell)
%o A068720 a068720 = a003415 . a000290  -- _Reinhard Zumkeller_, Mar 18 2014
%Y A068720 Cf. A000290, A003415, A068719, A068721, A235711.
%K A068720 nonn,easy
%O A068720 1,2
%A A068720 _Reinhard Zumkeller_, Feb 26 2002