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%I #7 Sep 26 2021 08:14:06
%S 1,1,1,1,4,1,1,1,9,1,1,4,9,1,1,1,1,1,4,25,1,1,4,9,2,25,36,1,1,1,9,1,
%T 25,9,49,1,1,4,1,4,25,4,49,16,1,1,1,9,4,1,9,49,1,27,1,1,4,9,2,25,36,
%U 49,16,27,100,1,1,1,1,1,25,1,49,4,9,25,121,1
%N Triangular array, read by rows: T(n,k) = denominator of arithmetic derivative of n/k, 1<=k<=n.
%C Arithmetic derivative of n/k = (k*A003415(n)-n*A003415(k))/k^2;
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuotientRule.html">Quotient Rule.</a>
%e ......................... 0
%e ................... 1 ........ 0
%e ............... 1 .... -1/4 ....... 0
%e ........... 4 ..... 1 ...... 8/9 ....... 0
%e ....... 1 ... -3/4 ... -2/9 ...... -1 ...... 0
%e ... 5 ..... 1 ..... 1 ..... -1/4 .... 19/25 .... 0
%e 1 .. -5/4 ... -4/9 ... -3/2 ... -2/25 ... -29/36 ... 0.
%t ader[n_Integer] := ader[n] = Switch[n, 0|1, 0, _, If[PrimeQ[n], 1, Sum[Module[{p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
%t ader[Rational[n_, k_]] := (ader[n] k - ader[k] n)/k^2;
%t T[n_, k_] := ader[n/k] // Denominator;
%t Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 26 2021 *)
%Y Numerator=A084884, A084887.
%K nonn,tabl
%O 1,5
%A _Reinhard Zumkeller_, Jun 10 2003
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