A125704 -id:A125704 - cp's OEIS frontend

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

Leroy Quet, Jan 31 2007

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.

			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,...

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 *)

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

Extended by Ray Chandler, Feb 07 2007

A126253 a(n) = n-th integer from among those positive integers which are each coprime to exactly one prime dividing n.

Original entry on oeis.org

3, 4, 7, 6, 10, 8, 15, 13, 18, 12, 22, 14, 26, 36, 31, 18, 34, 20, 38, 54, 42, 24, 46, 31, 50, 40, 54, 30, 130, 32, 63, 88, 66, 120, 70, 38, 74, 105, 78, 42, 192, 44, 86, 111, 90, 48, 94, 57, 98, 141, 102, 54, 106, 210, 110, 159, 114, 60, 255, 62, 122, 162

Offset: 2

Leroy Quet, Mar 08 2007

nonn

			The positive integers which are each coprime to exactly one prime dividing 12 form the sequence: 2,3,4,8,9,10,14,15,16,20,21,22,26,27,28... The 12th of these is 22; so a(12) = 22.

Cf. A125704, A128487.

a(n) = {ok = 0; nb = 0; i = 1; pf = factor(n)[,1]; while(! ok, if (sum(j=1, #pf, gcd(i, pf[j]) == 1) == 1, nb++); if (nb == n, ok = 1, i++);); i;} \\ Michel Marcus, Feb 10 2014

Offset corrected and more terms from Michel Marcus, Feb 10 2014

cp's OEIS Frontend

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.

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