A125703 Table read by antidiagonals: row n contains the positive integers (in order) which are coprime to the n-th prime and do not occur in earlier rows.

1, 2, 3, 6, 4, 5, 30, 12, 8, 7, 210, 60, 18, 10, 9, 2310, 420, 90, 24, 14, 11, 30030, 4620, 630, 120, 36, 16, 13, 510510, 60060, 6930, 840, 150, 42, 20, 15, 9699690, 1021020, 90090, 9240, 1050, 180, 48, 22, 17, 223092870, 19399380, 1531530, 120120, 11550

Offset: 1

Author

Leroy Quet, Jan 31 2007

Keywords

• nonn
• tabl

Comments

Row n, for n >= 2, contains the multiples of (product{k=1 to n-1} p(k)) that are coprime to p(n), where p(k) is the k-th prime. The concatenated sequence is a permutation of the positive integers.

Examples

			The beginning of the table:
1,3,5,7,9,11,...
2,4,8,10,14,16,20,...
6,12,18,24,36,...
30,60,90,120,150,...
210,420,630,840,...
		

Programs

Mathematica

f[n_, m_] := Block[{p = Prime[n], x = Product[Prime[i], {i, n - 1}], k = 0, c = m},While[c > 0,k += x;While[GCD[k, p] > 1, k += x];c--;];k];Table[f[d + 1 - m, m], {d, 10}, {m, d}] // Flatten (* Ray Chandler, Feb 07 2007 *)

Formula

T(n,m) = A002110(n-1)*A125704(n,m). - Ray Chandler, Feb 07 2007

Extensions

Extended by Ray Chandler, Feb 07 2007