A076221 Triangle read by rows: A(n,k) is the number of x, x<=n, which are coprime to and not equal to k.

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

Offset

1,4

Comments

Last entry of each row is Euler totient function phi(n).

{{0}, {1, 1}, {2, 2, 2}, {3, 2, 3, 2}, {4, 3, 4, 3, 4}, {5, 3, 4, 3, 5, 2}}

Links

Robert Israel, Table of n, a(n) for n = 1..10011

Example

a(20)=A(6,5) is 5 because (1,5), (2,5), (3,5), (4,5) and (5,6) are the five pairs of relatively primes integers <= 6.
Triangle begins:
  0,
  1, 1,
  2, 2, 2,
  3, 2, 3, 2,
  4, 3, 4, 3, 4,
  5, 3, 4, 3, 5, 2,
  ...

Maple

f:= proc(n, k) if k=1 then n-1 else  nops(select(t -> igcd(k, t)=1, [$1..n])) fi end proc:
seq(seq(f(n, k), k=1..n), n=1..30); # Robert Israel, Aug 29 2016

Mathematica

A[n_, k_] := Count[Range[n], x_ /; CoprimeQ[x, k] && x != k];
Table[A[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 05 2019 *)

Crossrefs

Sequence in context: A175872 A143117 A108053 * A029235 A289052 A329046

Adjacent sequences: A076218 A076219 A076220 * A076222 A076223 A076224

Keyword

nonn,tabl

Author

Olivier Gérard

Extensions

Definition and example corrected by Robert Israel, Aug 29 2016

Status

approved