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Largest gcd of two distinct numbers on row n of Pascal's triangle.
1

%I #15 Aug 26 2024 09:53:31

%S 1,1,2,5,5,7,28,42,42,165,132,429,1001,1001,1430,6188,4862,25194,

%T 41990,58786,58786,245157,653752,742900,1931540,4345965,2674440,

%U 17298645,9694845,29464725,94287120,129644790,927983760,811985790,477638700

%N Largest gcd of two distinct numbers on row n of Pascal's triangle.

%H Michael De Vlieger, <a href="/A092394/b092394.txt">Table of n, a(n) for n = 2..1000</a>

%e For n = 6, the numbers on the row are 1, 6, 15 and 20 and the gcd's of pairs of these are 1, 3, 2 and 5. So a(6) = 5.

%t Max /@ (GCD[#1, #2] & @@@ Subsets[#, {2}] & /@ Table[Binomial[n, k], {n, 2, 36}, {k, 0, Floor[n/2]}]) (* _Michael De Vlieger_, Feb 26 2016 *)

%o (PARI) mg(n) = {my(m = 0, v = vecsort(vector(n+1, k, k--; binomial(n,k)),,8));for (k=2, #v, for (j=1, k-1, m = max(m, gcd(v[k], v[j])););); m;} \\ _Michel Marcus_, Feb 26 2016

%Y Cf. A007318, A091963.

%K easy,nonn

%O 2,3

%A _David Wasserman_, Mar 21 2004