OFFSET
1,3
COMMENTS
Read by upwards antidiagonals as A(1,1), A(2,1), A(1,2), A(3,1), A(2,2), A(1,3), etc.
Seen as a triangle, the rows appear to be the reversed rows of the regular triangle defined by t(n,k) = denominator(n*k/(n-k)) for n>=2 and 1<=k<n. - Michel Marcus, Mar 24 2022
LINKS
EXAMPLE
The top left 18 x 18 corner of the array:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2
1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18
1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 17, 18
1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2
1, 1, 3, 1, 1, 3, 7, 1, 9, 1, 11, 3, 13, 7, 3, 1, 17, 9
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18
1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 14, 15, 16, 17, 18
1, 1, 3, 1, 5, 3, 1, 1, 9, 5, 11, 3, 13, 1, 15, 1, 17, 9
1, 2, 1, 4, 1, 2, 7, 8, 1, 2, 11, 4, 13, 14, 1, 16, 17, 2
1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18
1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
...
A(12,1) = 12 because d=12 is the largest divisor of 12 for which gcd(d,1) = 1.
A(12,2) = 3 because d=3 is the largest divisor of 12 for which gcd(d,2) = 1.
A(12,3) = 4 because d=4 is the largest divisor of 12 for which gcd(d,3) = 1.
A(12,4) = 3 because d=3 is the largest divisor of 12 for which gcd(d,4) = 1.
A(12,6) = 1 because d=1 is the largest divisor of 12 for which gcd(d,6) = 1.
MATHEMATICA
t[n_, m_] := Last[Select[Divisors[m], GCD[ #, n] == 1 &]]; Flatten[Table[t[i + 1 - j, j], {i, 15}, {j, i}]] (* Ray Chandler, Oct 17 2006 *)
PROG
(Python)
# Produces the triangle when the array is read by antidiagonals (upwards)
from sympy.ntheory import divisors
from math import gcd
def T(n, m):
return [i for i in divisors(m) if gcd(i, n)==1][-1]
for i in range(1, 16):
print([T(i+1-j, j) for j in range(1, i+1)]) # Indranil Ghosh, Mar 22 2017
(Scheme)
;; A naive implementation of A020639 given under that entry. The result of (A123275bi b a) is a product of all those prime factors of a (possibly occurring multiple times) that are not prime factors of b:
(define (A123275bi b a) (let loop ((a a) (m 1)) (let ((s (A020639 a))) (cond ((= 1 a) m) ((zero? (modulo b s)) (loop (/ a s) m)) (else (loop (/ a s) (* s m)))))))
;; Antti Karttunen, Mar 22 2017
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Leroy Quet, Oct 10 2006
EXTENSIONS
Extended by Ray Chandler, Oct 17 2006
Name and Example section edited by Antti Karttunen, Mar 22 2017
STATUS
approved