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 A287957 #14 Jun 04 2017 16:38:44 %S A287957 1,1,1,1,2,1,1,1,1,1,1,2,3,2,1,1,1,1,1,1,1,1,2,1,4,1,2,1,1,1,3,1,1,3, %T A287957 1,1,1,2,1,2,5,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,3,2,1,6,1,2,3,2,1,1,1, %U A287957 1,1,1,1,1,1,1,1,1,1,1,2,1,2,1,2,7,2,1 %N A287957 Table read by antidiagonals: T(n, k) = greatest common recursive divisor of n and k; n > 0 and k > 0. %C A287957 We use the definition of recursive divisor given in A282446. %C A287957 More informally, the prime tower factorization of T(n, k) is the intersection of the prime tower factorizations of n and k (the prime tower factorization of a number is defined in A182318). %C A287957 This sequence has connections with the classical GCD (A003989). %C A287957 For any i > 0, j > 0 and k > 0: %C A287957 - T(i, j) = 1 iff gcd(i, j) = 1, %C A287957 - A007947(T(i, j)) = A007947(gcd(i, j)), %C A287957 - T(i, j) >= 1, %C A287957 - T(i, j) <= min(i, j), %C A287957 - T(i, j) <= gcd(i, j), %C A287957 - T(i, 1) = 1, %C A287957 - T(i, i) = i, %C A287957 - T(i, j) = T(j, i) (the sequence is commutative), %C A287957 - T(i, T(j, k)) = T(T(i, j), k) (the sequence is associative), %C A287957 - T(i, i*j) <= i, %C A287957 - if gcd(i, j) = 1 then T(i*j, k) = T(i, k) * T(j, k) (the sequence is multiplicative), %C A287957 - T(i, 2*i) = A259445(i). %C A287957 See also A287958 for the LCM equivalent. %H A287957 Rémy Sigrist, <a href="/A287957/b287957.txt">First 100 antidiagonals of array, flattened</a> %H A287957 Rémy Sigrist, <a href="/A287957/a287957.pdf">Illustration of the first terms</a> %e A287957 Table starts: %e A287957 n\k| 1 2 3 4 5 6 7 8 9 10 %e A287957 ---+----------------------------------------------- %e A287957 1 | 1 1 1 1 1 1 1 1 1 1 ... %e A287957 2 | 1 2 1 2 1 2 1 2 1 2 ... %e A287957 3 | 1 1 3 1 1 3 1 1 3 1 ... %e A287957 4 | 1 2 1 4 1 2 1 2 1 2 ... %e A287957 5 | 1 1 1 1 5 1 1 1 1 5 ... %e A287957 6 | 1 2 3 2 1 6 1 2 3 2 ... %e A287957 7 | 1 1 1 1 1 1 7 1 1 1 ... %e A287957 8 | 1 2 1 2 1 2 1 8 1 2 ... %e A287957 9 | 1 1 3 1 1 3 1 1 9 1 ... %e A287957 10 | 1 2 1 2 5 2 1 2 1 10 ... %e A287957 ... %e A287957 T(4, 8) = T(2^2, 2^3) = 2. %o A287957 (PARI) T(n,k) = my (g=factor(gcd(n,k))); return (prod(i=1, #g~, g[i,1]^T(valuation(n, g[i,1]), valuation(k, g[i,1])))) %Y A287957 Cf. A003989, A007947, A182318, A259445, A282446, A287958. %K A287957 nonn,tabl,mult %O A287957 1,5 %A A287957 _Rémy Sigrist_, Jun 03 2017