%I #12 Nov 01 2020 04:11:57

%S 0,0,0,0,1,5,4,23,12,10,36,62,87,20,120,130,289,35,284,432,235,200,

%T 356,682,56,555,1256,385,1005,795,1330,84,960,2775,588,2939,1501,1844,

%U 2297,120,3436,1526,4304,1720,5205,852,6514,2538,5001,3647,165,7341,2280,2280,11712

%N a(n) is the number of ordered triples of divisors d_i < d_j < d_k of m such that GCD(d_i, d_j, d_k) > 1 where m is the least number having its prime signature; m = A025487(n).

%C Primitive sequence to A336530 as that sequence only depends on the prime signature of n.

%H David A. Corneth, <a href="/A338509/b338509.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A336530(A025487(n)).

%e a(6) = 12 as A025487(6) = 12 and there are 5 triples of divisors of 12 (x, y, z) such that g = gcd(x, y, z) are 12. 4 of them have g = 2 as 12/2 = 6 has 4 divisors and binomial(4, 3) = 4, 1 of them has g = 3 as 12/3 = 4 has 3 divisors and binomial(3, 3) = 1 and 0 of them have g = 6 as 12/6 = 2 has 3 divisors and binomial(2, 3) = 0.

%Y Cf. A025487, A336530.

%K nonn,easy

%O 1,6

%A _David A. Corneth_, Oct 31 2020