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A242224
Triangular array T read by rows, T(n, k) = n*k*(gcd(n,k)+2)/gcd(n,k)^2.
1
3, 6, 4, 9, 18, 5, 12, 8, 36, 6, 15, 30, 45, 60, 7, 18, 12, 10, 24, 90, 8, 21, 42, 63, 84, 105, 126, 9, 24, 16, 72, 12, 120, 48, 168, 10, 27, 54, 15, 108, 135, 30, 189, 216, 11, 30, 20, 90, 40, 14, 60, 210, 80, 270, 12, 33, 66, 99, 132, 165, 198, 231, 264, 297, 330, 13
OFFSET
1,1
COMMENTS
Described in the CNRS link as a puzzle where op(n,k) is defined by: op(n,n)=n+2, op(n,k)=op(k,n) and op(n,n+k)/op(n,k)=(n+k)/k.
If gcd(n,k)+2 is replaced by gcd(n,k), then triangle A051173 is obtained.
LINKS
Ana Rechtman, Mai, 1er défi, Images des Mathématiques, CNRS, 2014 (in French).
See also Comments, Images des Mathématiques, CNRS, 2014.
EXAMPLE
Triangle begins:
3;
6, 4;
9, 18, 5;
12, 8, 36, 6;
15, 30, 45, 60, 7;
18, 12, 10, 24, 90, 8;
...
MATHEMATICA
t[n_, k_] := n*k*(GCD[n, k] +2)/GCD[n, k]^2; Table[ t[n, k], {n, 12}, {k, n}] // Flatten (* Robert G. Wilson v, Jan 21 2018 *)
PROG
(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(n*k*(gcd(n, k)+2)/gcd(n, k)^2, ", "); ); print(); ); }
CROSSREFS
Sequence in context: A083349 A065230 A316478 * A294671 A275985 A163294
KEYWORD
nonn,tabl
AUTHOR
Michel Marcus, May 08 2014
STATUS
approved