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

-1, 1, 3, 5, 7, 11, 11, 17, 23, 29, 19, 23, 27, 31, 39, 29, 49, 59, 79, 89, 109, 41, 47, 53, 59, 65, 71, 83, 55, 69, 83, 97, 111, 125, 139, 153, 71, 79, 95, 103, 119, 127, 143, 151, 167, 89, 107, 143, 161, 179, 197, 233, 251, 269, 287, 109, 119, 129, 139

Offset: 1

Author

Reinhard Zumkeller, Aug 04 2015

Keywords

• sign
• tabl

Comments

For n > 1: T(n,1) = A028387(n-2).

Examples

			.   1:   -1
.   2:    1    3
.   3:    5    7   11
.   4:   11   17   23   29
.   5:   19   23   27   31   39
.   6:   29   49   59   79   89  109
.   7:   41   47   53   59   65   71   83
.   8:   55   69   83   97  111  125  139  153
.   9:   71   79   95  103  119  127  143  151  167
.  10:   89  107  143  161  179  197  233  251  269  287
.  11:  109  119  129  139  149  159  169  179  189  199  219
.  12:  131  175  197  241  263  307  329  373  395  439  461  505 .
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
• Eric Weisstein's World of Mathematics, Frobenius Number.
• Wikipedia, Coin problem

Crossrefs

Cf. A077664, A028387.

Programs

Haskell

a260910 n k = a260910_tabl !! (n - 1) !! (k-1)
a260910_row n = a260910_tabl !! (n-1)
a260910_tabl = zipWith (map . sylvester) [1..] a077664_tabl where
   sylvester u v = u * v - u - v

Mathematica

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[n_, k_] := (n-1) row[n][[k]] - n;
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 21 2021 *)

Formula

T(n,k) = (n-1) * A077664(n,k) - n.