OFFSET
1,4
COMMENTS
T(n,k) is the number of pairs (a,b), where 0 <= a < n, 0 <= b < k, gcd(a,n) != 1, and gcd(b,k) != 1. - Joerg Arndt, Jun 26 2011
LINKS
Nathaniel Johnston, Rows 1..100, flattened
FORMULA
EXAMPLE
First few rows of the triangle:
1;
1, 1;
2, 2, 4;
2, 2, 4, 4;
4, 4, 8, 8, 16;
2, 2, 4, 4, 8, 4;
6, 6, 12, 12, 24, 12, 36;
4, 4, 8, 8, 16, 8, 24, 16;
6, 6, 12, 12, 24, 12, 36, 24, 36;
...
T(7,5) = 24 = phi(7) * phi(5) = 6 * 4.
MAPLE
with(numtheory): T := proc(n, k) return phi(n)*phi(k): end: seq(seq(T(n, k), k=1..n), n=1..12); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
A143230[n_, k_]:= EulerPhi[n]*EulerPhi[k];
Table[A143230[n, k], {n, 12}, {k, n}] // Flatten (* G. C. Greubel, Sep 10 2024 *)
PROG
(Magma)
A143230:= func< n, k | EulerPhi(n)*EulerPhi(k) >;
[A143230(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Sep 10 2024
(SageMath)
def A143230(n, k): return euler_phi(n)*euler_phi(k)
flatten([[A143230(n, k) for k in range(1, n+1)] for n in range(1, 13)]) # G. C. Greubel, Sep 10 2024
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Jul 31 2008
STATUS
approved