|
| |
| |
|
|
|
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, 4, 4, 8, 8, 16, 8, 24, 16, 24, 16, 10, 10, 20, 20, 40, 20, 60, 40, 60, 40, 100, 4, 4, 8, 8, 16, 8, 24, 16, 24, 16, 40, 16
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| Left border = A000010.
Row sums = A143231: (1, 2, 8, 12, 40, 24,...).
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
| Triangle read by rows, A130207 * A000012 * A130207, where A130207 = A000010 * 0^(n-k), 1<=k<=n.
T(n,k) = phi(n) * phi(k), where phi(n) & phi(k) = Euler's totient function.
|
|
|
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
|
|
|
CROSSREFS
| Cf. A000010, A130207, A143231.
Sequence in context: A077659 A087692 A093621 * A072301 A127171 A118232
Adjacent sequences: A143227 A143228 A143229 * A143231 A143232 A143233
|
|
|
KEYWORD
| nonn,easy,tabl
|
|
|
AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 31 2008
|
| |
|
|
