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, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
[ 2] 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24
[ 3] 3, 6, 7, 12, 15, 14, 21, 24, 19, 30, 33, 28
[ 4] 4, 8, 12, 14, 20, 24, 28, 26, 36, 40, 44, 42
[ 5] 5, 10, 15, 20, 13, 30, 35, 40, 45, 26, 55, 60
[ 6] 6, 12, 14, 24, 30, 28, 42, 48, 38, 60, 66, 56
[ 7] 7, 14, 21, 28, 35, 42, 19, 56, 63, 70, 77, 84
[ 8] 8, 16, 24, 26, 40, 48, 56, 42, 72, 80, 88, 78
[ 9] 9, 18, 19, 36, 45, 38, 63, 72, 37, 90, 99, 76
[10] 10, 20, 30, 40, 26, 60, 70, 80, 90, 52, 110, 120
[11] 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 31, 132
[12] 12, 24, 28, 42, 60, 56, 84, 78, 76, 120, 132, 98
.
Displayed as a triangular array:
1,
2, 2,
3, 4, 3,
4, 6, 6, 4,
5, 8, 7, 8, 5,
6, 10, 12, 12, 10, 6,
7, 12, 15, 14, 15, 12, 7,
8, 14, 14, 20, 20, 14, 14, 8,
9, 16, 21, 24, 13, 24, 21, 16, 9,
MAPLE
with(numtheory):
T:= (n, k)-> add(add(phi(ilcm(c, d)), c=divisors(n)), d=divisors(k)):
seq (seq (T(n, 1+d-n), n=1..d), d=1..14); # Alois P. Heinz, Sep 12 2012
MATHEMATICA
t[n_, k_] := Sum[ EulerPhi[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, Jun 28 2013 *)
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 12 2012
STATUS
approved