This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A123275 #46 Mar 24 2022 10:29:49
%S A123275 1,1,2,1,1,3,1,2,3,4,1,1,1,1,5,1,2,3,4,5,6,1,1,3,1,5,3,7,1,2,1,4,5,2,
%T A123275 7,8,1,1,3,1,1,3,7,1,9,1,2,3,4,5,6,7,8,9,10,1,1,1,1,5,1,7,1,1,5,11,1,
%U A123275 2,3,4,5,6,7,8,9,10,11,12,1,1,3,1,5,3,1,1,9,5,11,3,13,1,2,1,4,1,2,7,8,1,2
%N A123275 Square array A(n,m) = largest divisor of m which is coprime to n, read by upwards antidiagonals.
%C A123275 Read by upwards antidiagonals as A(1,1), A(2,1), A(1,2), A(3,1), A(2,2), A(1,3), etc.
%C A123275 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
%H A123275 Antti Karttunen, <a href="/A123275/b123275.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a>
%e A123275 The top left 18 x 18 corner of the array:
%e A123275 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18
%e A123275 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
%e A123275 1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2
%e A123275 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
%e A123275 1, 2, 3, 4, 1, 6, 7, 8, 9, 2, 11, 12, 13, 14, 3, 16, 17, 18
%e A123275 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
%e A123275 1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 11, 12, 13, 2, 15, 16, 17, 18
%e A123275 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
%e A123275 1, 2, 1, 4, 5, 2, 7, 8, 1, 10, 11, 4, 13, 14, 5, 16, 17, 2
%e A123275 1, 1, 3, 1, 1, 3, 7, 1, 9, 1, 11, 3, 13, 7, 3, 1, 17, 9
%e A123275 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 12, 13, 14, 15, 16, 17, 18
%e A123275 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
%e A123275 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 14, 15, 16, 17, 18
%e A123275 1, 1, 3, 1, 5, 3, 1, 1, 9, 5, 11, 3, 13, 1, 15, 1, 17, 9
%e A123275 1, 2, 1, 4, 1, 2, 7, 8, 1, 2, 11, 4, 13, 14, 1, 16, 17, 2
%e A123275 1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, 3, 13, 7, 15, 1, 17, 9
%e A123275 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 1, 18
%e A123275 1, 1, 1, 1, 5, 1, 7, 1, 1, 5, 11, 1, 13, 7, 5, 1, 17, 1
%e A123275 ...
%e A123275 A(12,1) = 12 because d=12 is the largest divisor of 12 for which gcd(d,1) = 1.
%e A123275 A(12,2) = 3 because d=3 is the largest divisor of 12 for which gcd(d,2) = 1.
%e A123275 A(12,3) = 4 because d=4 is the largest divisor of 12 for which gcd(d,3) = 1.
%e A123275 A(12,4) = 3 because d=3 is the largest divisor of 12 for which gcd(d,4) = 1.
%e A123275 A(12,6) = 1 because d=1 is the largest divisor of 12 for which gcd(d,6) = 1.
%t A123275 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 *)
%o A123275 (Python)
%o A123275 # Produces the triangle when the array is read by antidiagonals (upwards)
%o A123275 from sympy.ntheory import divisors
%o A123275 from math import gcd
%o A123275 def T(n,m):
%o A123275 return [i for i in divisors(m) if gcd(i,n)==1][-1]
%o A123275 for i in range(1, 16):
%o A123275 print([T(i+1-j, j) for j in range(1, i+1)]) # _Indranil Ghosh_, Mar 22 2017
%o A123275 (Scheme)
%o A123275 ;; 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:
%o A123275 (define (A123275 n) (A123275bi (A004736 n) (A002260 n)))
%o A123275 (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)))))))
%o A123275 ;; _Antti Karttunen_, Mar 22 2017
%Y A123275 Cf. A003989, A020639, A243103.
%K A123275 nonn,tabl
%O A123275 1,3
%A A123275 _Leroy Quet_, Oct 10 2006
%E A123275 Extended by _Ray Chandler_, Oct 17 2006
%E A123275 Name and Example section edited by _Antti Karttunen_, Mar 22 2017