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A076221
Triangle read by rows: A(n,k) is the number of x, x<=n, which are coprime to and not equal to k.
7
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
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
KEYWORD
nonn,tabl
EXTENSIONS
Definition and example corrected by Robert Israel, Aug 29 2016
STATUS
approved