A377188 Triangle read by rows: T(n,k) = denominator((n^2 + k)/(n^2 - k)).
1, 7, 1, 7, 13, 3, 23, 11, 21, 2, 17, 11, 4, 31, 5, 47, 23, 45, 22, 43, 3, 31, 61, 15, 59, 29, 57, 7, 79, 13, 77, 38, 25, 37, 73, 4, 49, 97, 12, 19, 47, 93, 23, 91, 9, 119, 59, 117, 58, 115, 57, 113, 56, 111, 5, 71, 47, 35, 139, 23, 137, 17, 15, 67, 133, 11
Offset: 2
Examples
The triangle begins as: 1; 7, 1; 7, 13, 3; 23, 11, 21, 2; 17, 11, 4, 31, 5; 47, 23, 45, 22, 43, 3; 31, 61, 15, 59, 29, 57, 7; 79, 13, 77, 38, 25, 37, 73, 4; 49, 97, 12, 19, 47, 93, 23, 91, 9; ...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.3, p. 14.
Programs
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Mathematica
T[n_,k_]:=Denominator[(n^2+k)/(n^2-k)]; Table[T[n,k],{n,2,12},{k,2,n}]//Flatten -
Python
from math import isqrt, comb, gcd def A377188(n): return (d:=(a:=(m:=isqrt(k:=n-1<<1))+(k>m*(m+1))+1)**2-(b:=n-comb(a-1,2)))//gcd(d,d+(b<<1)) # Chai Wah Wu, Nov 12 2024