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A143230 Triangle read by rows, A130207 * A000012 * A130207. 2
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; text; 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
Sequence in context: A093621 A242734 A309709 * A276604 A072301 A127171
KEYWORD
nonn,easy,tabl
AUTHOR
Gary W. Adamson, Jul 31 2008
STATUS
approved

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Last modified July 20 18:59 EDT 2024. Contains 374459 sequences. (Running on oeis4.)