A125704 Table read by antidiagonals: row n contains the positive integers (in order) which are coprime to the n-th prime.

1, 1, 3, 1, 2, 5, 1, 2, 4, 7, 1, 2, 3, 5, 9, 1, 2, 3, 4, 7, 11, 1, 2, 3, 4, 6, 8, 13, 1, 2, 3, 4, 5, 7, 10, 15, 1, 2, 3, 4, 5, 6, 8, 11, 17, 1, 2, 3, 4, 5, 6, 8, 9, 13, 19, 1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 21, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 25, 1, 2, 3, 4, 5

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150).

Formula

T(1,m) = A005408(m). T(2,m) = A001651(m). T(3,m) = A047201(m). T(4,m) = A047304(m). - R. J. Mathar, Feb 02 2007

T(n,m) = m - 1 + floor((m+prime(n)-2)/(prime(n)-1)) where prime(n) = n-th prime. - Benoit Cloitre, Jul 11 2009

Example

Beginning of table:
  1,  3,  5,  7,  9, 11, 13, ...
  1,  2,  4,  5,  7,  8, 10, 11, ...
  1,  2,  3,  4,  6,  7,  8,  9, 11, ...
  1,  2,  3,  4,  5,  6,  8,  9, 10, ...

Maple

A125704 := proc(n, m) local p, i, a ; p := ithprime(n) ; a := 1 ; for i from 2 to m do a := a+1 ; while gcd(a, p) <> 1 do a := a+1 ; od ; od ; RETURN(a) ; end : maxdiag := 15 ; for d from 1 to maxdiag do for n from d to 1 by -1 do printf("%d, ", A125704(n, d-n+1)) ; od ; od; # R. J. Mathar, Feb 02 2007

Mathematica

Table[Function[n, k - 1 + Floor[(k + Prime[n] - 2)/(Prime[n] - 1)]][m - k + 1], {m, 14}, {k, m}] // Flatten (* Michael De Vlieger, Oct 10 2017, after PARI by Benoit Cloitre *)

Prog

(PARI) T(n, m)=m-1+floor((m+prime(n)-2)/(prime(n)-1)) \\ Benoit Cloitre, Jul 11 2009

Crossrefs

Sequence in context: A021036 A354348 A211025 * A357498 A131127 A113141

Adjacent sequences: A125701 A125702 A125703 * A125705 A125706 A125707

Keyword

nonn,tabl

Author

Leroy Quet, Jan 31 2007

Extensions

More terms from R. J. Mathar, Feb 02 2007

Status

approved