A127368 Relative prime triangle, read by rows.

1, 1, 0, 1, 2, 0, 1, 0, 3, 0, 1, 2, 3, 4, 0, 1, 0, 0, 0, 5, 0, 1, 2, 3, 4, 5, 6, 0, 1, 0, 3, 0, 5, 0, 7, 0, 1, 2, 0, 4, 5, 0, 7, 8, 0, 1, 0, 3, 0, 0, 0, 7, 0, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 0, 0, 0, 5, 0, 7, 0, 0, 0, 11, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 0

Offset: 1

Author

Gary W. Adamson, Jan 11 2007

Keywords

• nonn
• easy
• tabl

Comments

Row sums = A023896, (reduced residue system mod n): (1, 1, 3, 4, 10, 6, 21, ...). - Gary W. Adamson, Aug 27 2008

Examples

			Row 4 = (1, 0, 3, 0) since 1 and 3 are relative primes of 4.
First few rows of the triangle are:
  1;
  1, 0;
  1, 2, 0;
  1, 0, 3, 0;
  1, 2, 3, 4, 0;
  1, 0, 0, 0, 5, 0;
  1, 2, 3, 4, 5, 6, 0;
  ...
		

Crossrefs

Cf. A054521, A023896.

Programs

PARI

T127368(n,k)={gcd(n,k)==1 & return(k)}
A127368(n)=T127368( t=(sqrt(8*n)+1)\2, n-binomial(t, 2)) \\ M. F. Hasler, Mar 02 2012

Formula

T(n,k) = k if a relative prime of n; 0 otherwise. Replace the "1's" of A054521 with their corresponding column numbers; leaving the zeros.

Equals A054521 * A127648 as infinite lower triangular matrices. - Gary W. Adamson, Aug 27 2008

Extensions

Corrected at the suggestion of Kevin Ryde by Alois P. Heinz, Mar 02 2012