OFFSET
1,2
COMMENTS
LINKS
Alois P. Heinz, Antidiagonals n = 1..141, flattened
EXAMPLE
[-----1---2---3----4----5----6----7----8----9---10---11---12]
[ 1] 1, 3, 4, 7, 6, 12, 8, 15, 13, 18, 12, 28
[ 2] 3, 7, 12, 15, 18, 28, 24, 31, 39, 42, 36, 60
[ 3] 4, 12, 10, 28, 24, 30, 32, 60, 28, 72, 48, 70
[ 4] 7, 15, 28, 27, 42, 60, 56, 51, 91, 90, 84, 108
[ 5] 6, 18, 24, 42, 16, 72, 48, 90, 78, 48, 72, 168
[ 6] 12, 28, 30, 60, 72, 70, 96, 124, 84, 168, 144, 150
[ 7] 8, 24, 32, 56, 48, 96, 22, 120, 104, 144, 96, 224
[ 8] 15, 31, 60, 51, 90, 124, 120, 83, 195, 186, 180, 204
[ 9] 13, 39, 28, 91, 78, 84, 104, 195, 55, 234, 156, 196
[10] 18, 42, 72, 90, 48, 168, 144, 186, 234, 112, 216, 360
[11] 12, 36, 48, 84, 72, 144, 96, 180, 156, 216, 34, 336
[12] 28, 60, 70, 108, 168, 150, 224, 204, 196, 360, 336, 270
.
Displayed as a triangular array:
1;
3, 3;
4, 7, 4;
7, 12, 12, 7;
6, 15, 10, 15, 6;
12, 18, 28, 28, 18, 12;
8, 28, 24, 27, 24, 28, 8;
15, 24, 30, 42, 42, 30, 24, 15;
13, 31, 32, 60, 16, 60, 32, 31, 13;
MAPLE
with(numtheory):
T:= (n, k) -> add(add(ilcm(c, d), c=divisors(n)), d=divisors(k)):
seq (seq (T(n, 1+d-n), n=1..d), d=1..12); # Alois P. Heinz, Sep 12 2012
MATHEMATICA
T[n_, k_] := Sum[LCM[c, d], {c, Divisors[n]}, {d, Divisors[k]}]; Table[T[n-k+1, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 25 2014 *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 12 2012
STATUS
approved