A115957 Numbers k having exactly 3 distinct prime factors, the largest of which is greater than or equal to sqrt(k) (i.e., sqrt(k)-rough numbers with exactly 3 distinct prime factors).

42, 66, 78, 102, 110, 114, 130, 138, 156, 170, 174, 186, 190, 204, 222, 228, 230, 238, 246, 255, 258, 266, 276, 282, 285, 290, 310, 318, 322, 342, 345, 348, 354, 366, 370, 372, 402, 406, 410, 414, 426, 430, 434, 435, 438, 444, 460, 465, 470, 474, 483, 492

Offset: 1

Author

Emeric Deutsch, Feb 02 2006

Keywords

• nonn

Examples

			156 is in the sequence because it has 3 distinct prime factors (2, 3 and 13) and 13 > sqrt(156).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A115956, A115958, A115959, A115960, A115961.

Programs

Maple

with(numtheory): a:=proc(n) if nops(factorset(n))=3 and factorset(n)[3]^2>=n then n else fi end: seq(a(n),n=1..530);

Mathematica

Select[Range[500],PrimeNu[#]==3&&FactorInteger[#][[-1,1]]>=Sqrt[#]&] (* Harvey P. Dale, Apr 09 2019 *)