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.
%I A068328 #27 Mar 04 2024 01:34:20
%S A068328 0,1,1,1,5,1,7,1,1,9,8,1,1,10,13,1,15,1,31,1,14,19,12,1,21,16,1,41,1,
%T A068328 25,1,20,1,16,22,31,1,1,33,18,61,1,26,59,1,1,39,18,71,1,43,1,22,45,32,
%U A068328 1,20,34,49,24,1,1,91,1,71,55,1,1,87,40,1,101,28,61,24,63,44,1,46
%N A068328 Arithmetic derivatives of the squarefree numbers.
%C A068328 a(n) and A005117(n) are coprime, cf. A085731. - _Reinhard Zumkeller_, May 10 2011
%H A068328 Reinhard Zumkeller, <a href="/A068328/b068328.txt">Table of n, a(n) for n = 1..10000</a>
%H A068328 Victor Ufnarovski and Bo Ahlander, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html">How to Differentiate a Number</a>, J. Integer Seqs., Vol. 6 (2003), Article 03.3.4.
%F A068328 a(n) = A003415(A005117(n)).
%F A068328 a(n) = A069359(A005117(n)).
%F A068328 a(n) = Sum_{prime p | A005117(n)} A005117(n)/p.
%e A068328 a(65) = d(A005117(65)) = d(105) = d(3*35) = 3*d(35)+d(3)*35 = 3*d(5*7)+1*35 = 3*d(5*7)+1*35 = 3*(5*d(7)+d(5)*7)+35 = 3*(5*1+1*7)+35 = 3*12+35 = 71, where d(n) = A003415(n).
%e A068328 With d(1)=0, d(prime) = 1 and d(m*n) = d(m)*n + m*d(n).
%t A068328 ad[n_] := ad[n] = n*Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad[1] = 0; Table[ad[k], {k, Select[Range[150], SquareFreeQ]}] (* _Amiram Eldar_, Mar 04 2024 *)
%o A068328 (Haskell)
%o A068328 a068328 = a003415 . a005117 -- _Reinhard Zumkeller_, May 10 2011
%Y A068328 Cf. A003415, A005117, A069359, A085731.
%K A068328 nonn
%O A068328 1,5
%A A068328 _Reinhard Zumkeller_, Feb 27 2002