A127479 Triangle read by rows: T(n,k) = Sum_{d|n, gcd(d,k)==1, d>=k} phi(d).

1, 2, 0, 3, 2, 0, 4, 0, 2, 0, 5, 4, 4, 4, 0, 6, 2, 0, 0, 2, 0, 7, 6, 6, 6, 6, 6, 0, 8, 0, 6, 0, 4, 0, 4, 0, 9, 8, 0, 6, 6, 0, 6, 6, 0, 10, 4, 8, 4, 0, 0, 4, 0, 4, 0, 11, 10, 10, 10, 10, 10, 10, 10, 10, 10, 0, 12, 2, 2, 0, 6, 0, 4, 0, 0, 0, 4, 0, 13, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 0

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)

Formula

Equals A054522 * A054521 as infinite lower triangular matrices.

Example

First few rows of the triangle:
  1;
  2, 0;
  3, 2, 0;
  4, 0, 2, 0;
  5, 4, 4, 4, 0;
  6, 2, 0, 0, 2, 0;
  7, 6, 6, 6, 6, 6, 0;
  8, 0, 6, 0, 4, 0, 4, 0;
  ...

Prog

(PARI) T(n, k)=sumdiv(n, d, if(d>=k && gcd(d, k)==1, eulerphi(d))) \\ Andrew Howroyd, Sep 23 2025

Crossrefs

Row sums are A029939.

Cf. A000010, A054522, A054521.

Sequence in context: A035159 A103489 A213944 * A284124 A187637 A338737

Adjacent sequences: A127476 A127477 A127478 * A127480 A127481 A127482

Keyword

nonn,tabl

Author

Gary W. Adamson, Jan 15 2007

Extensions

Edited by N. J. A. Sloane, Aug 10 2019

New name and a(56) onwards from Andrew Howroyd, Sep 23 2025

Status

approved