A091717 - OEIS

%I #13 May 10 2020 03:30:39

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,5,1,1,1,1,2,1,1,1,

%T 11,1,1,1,2,3,5,1,1,15,2,1,1,2,3,1,7,1,3,2,6,1,1,2,1,1,7,1,1,2,2,14,1,

%U 1,1,1,1,7,11,1,11,1,7,7,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,3,5,1,1,15,1

%N Triangular array read by rows: Greatest common divisors of values of the partition function P: T(n,k) = gcd(P(n), P(k)), 0 <= k < n.

%H Amiram Eldar, <a href="/A091717/b091717.txt">Table of n, a(n) for n = 1..11175</a>, rows 1..150 in flattened form.

%F A091718(n) = Max_{k=0..n-1} T(n,k);

%F T(n,0) = T(n,1) = 1; T(n,n-1) = A091719(n-1).

%e Triangle begins:

%e 1

%e 1, 1

%e 1, 1, 1

%e 1, 1, 1, 1

%e 1, 1, 1, 1, 1

%e 1, 1, 1, 1, 1, 1

%e 1, 1, 1, 3, 5, 1, 1

%e 1, 1, 2, 1, 1, 1, 11, 1

%e ...

%t m = 15; p = PartitionsP[Range[0, m]]; Table[GCD[p[[i]], p[[j]]], {i, 1, m}, {j, 1, i - 1}] // Flatten (* _Amiram Eldar_, May 10 2020 *)

%Y Cf. A000041, A091718, A091719.

%K nonn,tabl

%O 1,25

%A _Reinhard Zumkeller_, Feb 01 2004