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

1,2

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.

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

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,...

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 *)

Crossrefs

Sequence in context: A209775 A360599 A306231 * A349381 A156688 A348243

Adjacent sequences: A125700 A125701 A125702 * A125704 A125705 A125706

Keyword

nonn,tabl

Author

Leroy Quet, Jan 31 2007

Extensions

Extended by Ray Chandler, Feb 07 2007

Status

approved