

A125703


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


0



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
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OFFSET

1,2


COMMENTS

Row n, for n >= 2, contains the multiples of (product{k=1 to n1} p(k)) that are coprime to p(n), where p(k) is the kth 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(n1)*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: A138153 A209775 A306231 * A156688 A019567 A098286
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



