login
A216627
Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = sum_{c|n,d|k} lcm(c,d).
8
1, 3, 7, 4, 12, 10, 7, 15, 28, 27, 6, 18, 24, 42, 16, 12, 28, 30, 60, 72, 70, 8, 24, 32, 56, 48, 96, 22, 15, 31, 60, 51, 90, 124, 120, 83, 13, 39, 28, 91, 78, 84, 104, 195, 55, 18, 42, 72, 90, 48, 168, 144, 186, 234, 112, 12, 36, 48, 84, 72, 144, 96, 180, 156
OFFSET
1,2
COMMENTS
This is the lower triangular array of A216626, which is the main entry for this sequence.
LINKS
FORMULA
T(n,1) = A000203(n) = sigma(n).
T(n,n) = A064950(n) = sum_{d|n} d*tau(d^2).
EXAMPLE
The first rows of the triangle are:
1;
3, 7;
4, 12, 10;
7, 15, 28, 27;
6, 18, 24, 42, 16;
12, 28, 30, 60, 72, 70;
8, 24, 32, 56, 48, 96, 22;
15, 31, 60, 51, 90, 124, 120, 83;
13, 39, 28, 91, 78, 84, 104, 195, 55;
MAPLE
with(numtheory):
T:= (n, k) -> add(add(ilcm(c, d), c=divisors(n)), d=divisors(k));
seq (seq (T(n, k), k=1..n), n=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], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 25 2014 *)
PROG
(Sage)
for n in (1..9): [A216626(n, k) for k in (1..n)]
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 12 2012
STATUS
approved