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URL: https://oeis.org/A242114

⇱ A242114 - OEIS

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A242114
Triangle read by rows: T(n,k) = number of pairs (x,y) in {1..n}X{1..n} with gcd(x,y) = k.
5
1, 3, 1, 7, 1, 1, 11, 3, 1, 1, 19, 3, 1, 1, 1, 23, 7, 3, 1, 1, 1, 35, 7, 3, 1, 1, 1, 1, 43, 11, 3, 3, 1, 1, 1, 1, 55, 11, 7, 3, 1, 1, 1, 1, 1, 63, 19, 7, 3, 3, 1, 1, 1, 1, 1, 83, 19, 7, 3, 3, 1, 1, 1, 1, 1, 1, 91, 23, 11, 7, 3, 3, 1, 1, 1, 1, 1, 1, 115, 23
OFFSET
1,2
COMMENTS
T(n,1) = A018805(n);
sum(T(n,k): k = 1..n) = A000290(n);
sum(T(n,k): k = 2..n) = A100613(n);
T(floor(n/k),1) = A018805(n).
LINKS
FORMULA
T(n,k) = A018805(A010766(n,k));
EXAMPLE
T(4,1) = #{(1,1), (1,2), (1,3), (1,4), (2,1), (2,3), (3,1), (3,2), (3,4), (4,1), (4,3)} = 11;
T(4,2) = #{(2,2), (2,4), (4,2)} = 3;
T(4,3) = #{(3,3)} = 1;
T(4,4) = #{(4,4)} = 1.
The triangle begins: row sums
. 1: 1 1
. 2: 3 1 4
. 3: 7 1 1 9
. 4: 11 3 1 1 16
. 5: 19 3 1 1 1 25
. 6: 23 7 3 1 1 1 36
. 7: 35 7 3 1 1 1 1 49
. 8: 43 11 3 3 1 1 1 1 64
. 9: 55 11 7 3 1 1 1 1 1 81
. 10: 63 19 7 3 3 1 1 1 1 1 100
. 11: 83 19 7 3 3 1 1 1 1 1 1 121
. 12: 91 23 11 7 3 3 1 1 1 1 1 1 144
. 13: 115 23 11 7 3 3 1 1 1 1 1 1 1 169
. 14: 127 35 11 7 3 3 3 1 1 1 1 1 1 1 196
. 15: 143 35 19 7 7 3 3 1 1 1 1 1 1 1 1 225
. 16: 159 43 19 11 7 3 3 3 1 1 1 1 1 1 1 1 256
. 17: 191 43 19 11 7 3 3 3 1 1 1 1 1 1 1 1 1 289
. 18: 203 55 23 11 7 7 3 3 3 1 1 1 1 1 1 1 1 1 324 .
MATHEMATICA
T[n_, k_] := 2 Total[EulerPhi[Range[Quotient[n, k]]]] - 1;
Table[T[n, k], {n, 1, 18}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 20 2021 *)
PROG
(Haskell)
a242114 n k = a242114_tabl !! (n-1) !! (k-1)
a242114_row n = a242114_tabl !! (n-1)
a242114_tabl = map (map a018805) a010766_tabl
CROSSREFS
Sequence in context: A346182 A026499 A339452 * A143470 A114580 A257597
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, May 04 2014
STATUS
approved