A338509 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).

0, 0, 0, 0, 1, 5, 4, 23, 12, 10, 36, 62, 87, 20, 120, 130, 289, 35, 284, 432, 235, 200, 356, 682, 56, 555, 1256, 385, 1005, 795, 1330, 84, 960, 2775, 588, 2939, 1501, 1844, 2297, 120, 3436, 1526, 4304, 1720, 5205, 852, 6514, 2538, 5001, 3647, 165, 7341, 2280, 2280, 11712

Offset: 1

Author

David A. Corneth, Oct 31 2020

Keywords

• nonn
• easy

Comments

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

Examples

			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.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A025487, A336530.

Formula

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