OFFSET
1,12
LINKS
Eric Weisstein's World of Mathematics, Quotient Rule.
EXAMPLE
............................. 0
....................... -1/4 ..... 0
................ -1/9 ...... 1/9 ...... 0
.... ...... -1/4 ..... -1/4 .... -1/2 ...... 0
.. .. -1/25 .... 3/25 ..... 2/25 ..... 16/25 .... 0
-5/36 ..... -1/9 ..... -1/4 ..... 1/9 .... -19/36 .... 0.
MATHEMATICA
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]}]]];
ader[Rational[n_, k_]] := (ader[n] k - ader[k] n)/k^2;
T[n_, k_] := ader[k/n] // Numerator;
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 26 2021 *)
CROSSREFS
KEYWORD
sign,tabl
AUTHOR
Reinhard Zumkeller, Jun 10 2003
STATUS
approved