OFFSET
1,2
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of triangle
FORMULA
As a triangle (with n >= 1, 1 <= k <= n):
T(n,k) = (1/2)*(2 + ((gcd(n,k)+lcm(n,k))^2) - gcd(n,k) - 3*lcm(n,k)).
EXAMPLE
The first twelve rows of the triangle:
1,
2, 5,
4, 16, 13,
7, 12, 67, 25,
11, 46, 106, 191, 41,
16, 23, 31, 80, 436, 61,
22, 92, 211, 379, 596, 862, 85,
29, 38, 277, 59, 781, 302, 1541, 113,
37, 154, 58, 631, 991, 193, 1954, 2557, 145,
46, 57, 436, 212, 96, 467, 2416, 822, 4006, 181,
56, 232, 529, 947, 1486, 2146, 2927, 3829, 4852, 5996, 221,
67, 80, 94, 109, 1771, 142, 3487, 355, 706, 1832, 8647, 265
----------------------------------------------------------------
For T(4,3) we have gcd(4,3) = 1 and lcm(4,3) = 12, thus T(4,3) = (1/2)*(2 + (12+1)^2 - 1 - 3*12) = 67.
For T(6,4) we have gcd(6,4) = 2 and lcm(6,4) = 12, thus T(6,4) = (1/2)*(2 + (12+2)^2 - 2 - 3*12) = 80.
For T(12,1) we have gcd(12,1) = 1 and lcm(12,1) = 12, thus T(12,1) = T(4,3) = 67.
For T(12,2) we have gcd(12,2) = 2 and lcm(12,1) = 12, thus T(12,1) = T(6,4) = 80.
For T(12,8) we have gcd(12,8) = 4 and lcm(12,8) = 24, thus T(12,8) = (1/2)*(2 + (24+4)^2 - 4 - 3*24) = 355.
PROG
(Python)
from sympy import lcm, gcd
def t(n, k): return (2 + ((gcd(n, k) + lcm(n, k))**2) - gcd(n, k) - 3*lcm(n, k))/2
for n in range(1, 21): print [t(n, k) for k in range(1, n + 1)] # Indranil Ghosh, May 11 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 06 2017
STATUS
approved