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

1,5

Comments

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

Links

Table of n, a(n) for n=1..91.

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

Example

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;
  ...

Prog

(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

Crossrefs

Cf. A054521, A023896.

Sequence in context: A108045 A298972 A143728 * A112552 A048154 A320602

Adjacent sequences: A127365 A127366 A127367 * A127369 A127370 A127371

Keyword

nonn,easy,tabl

Author

Gary W. Adamson, Jan 11 2007

Extensions

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

Status

approved