A336628 Numbers k that have 3 divisors d1, d2, d3 such that d1 < d2 < d3 < 2*d1 and are pairwise coprime and d1*d2*d3 = k.

60, 140, 210, 280, 315, 360, 462, 504, 616, 630, 693, 728, 770, 792, 819, 910, 924, 936, 990, 1001, 1092, 1144, 1170, 1287, 1320, 1386, 1430, 1530, 1560, 1584, 1638, 1683, 1716, 1870, 1872, 1989, 2002, 2090, 2142, 2145, 2210, 2244, 2288, 2310, 2431, 2448, 2470, 2508

Offset: 1

Author

David A. Corneth and Amiram Eldar, Jul 28 2020

Keywords

• nonn

Comments

(k/4)^(1/3) < d1 < k^(1/3). Proof: as k = d1 * d2 * d3 < d1 * (2*d1) * (2*d1) = 4*d1^3 we have (k/4)^(1/3) < d1 and as k = d1 * d2 * d3 > d1 * d1 * d1 = d1^3 we have k^(1/3) > d1. Q.e.d.

Examples

			210 is in the sequence because 5*6*7 = 210 and each of these factors are pairwise coprime and 5 < 6 < 7 < 2*5 = 10.
		

Crossrefs

Cf. A333966, A336629.