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A260910 Triangle read by rows: Fresenius numbers of n and A077664(n,k), k = 1..n.

%I A260910 #9 Feb 16 2025 08:33:26
%S A260910 -1,1,3,5,7,11,11,17,23,29,19,23,27,31,39,29,49,59,79,89,109,41,47,53,
%T A260910 59,65,71,83,55,69,83,97,111,125,139,153,71,79,95,103,119,127,143,151,
%U A260910 167,89,107,143,161,179,197,233,251,269,287,109,119,129,139
%N A260910 Triangle read by rows: Fresenius numbers of n and A077664(n,k), k = 1..n.
%C A260910 For n > 1: T(n,1) = A028387(n-2).
%H A260910 Reinhard Zumkeller, <a href="/A260910/b260910.txt">Rows n = 1..125 of triangle, flattened</a>
%H A260910 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FrobeniusNumber.html">Frobenius Number</a>.
%H A260910 Wikipedia, <a href="http://en.wikipedia.org/wiki/Coin_problem">Coin problem</a>
%F A260910 T(n,k) = (n-1) * A077664(n,k) - n.
%e A260910 .   1:   -1
%e A260910 .   2:    1    3
%e A260910 .   3:    5    7   11
%e A260910 .   4:   11   17   23   29
%e A260910 .   5:   19   23   27   31   39
%e A260910 .   6:   29   49   59   79   89  109
%e A260910 .   7:   41   47   53   59   65   71   83
%e A260910 .   8:   55   69   83   97  111  125  139  153
%e A260910 .   9:   71   79   95  103  119  127  143  151  167
%e A260910 .  10:   89  107  143  161  179  197  233  251  269  287
%e A260910 .  11:  109  119  129  139  149  159  169  179  189  199  219
%e A260910 .  12:  131  175  197  241  263  307  329  373  395  439  461  505 .
%t A260910 row[n_] := Module[{j, k}, Reap[For[j = n+1; k = 1, k <= n, j++, If[CoprimeQ[n, j], Sow[j]; k++]]][[2, 1]]];
%t A260910 T[n_, k_] := (n-1) row[n][[k]] - n;
%t A260910 Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Sep 21 2021 *)
%o A260910 (Haskell)
%o A260910 a260910 n k = a260910_tabl !! (n - 1) !! (k-1)
%o A260910 a260910_row n = a260910_tabl !! (n-1)
%o A260910 a260910_tabl = zipWith (map . sylvester) [1..] a077664_tabl where
%o A260910    sylvester u v = u * v - u - v
%Y A260910 Cf. A077664, A028387.
%K A260910 sign,tabl
%O A260910 1,3
%A A260910 _Reinhard Zumkeller_, Aug 04 2015