A115956 Numbers k having exactly 2 distinct prime factors, the largest of which is greater than or equal to sqrt(k) (i.e., sqrt(k)-rough numbers with exactly 2 distinct prime factors).
6, 10, 14, 15, 20, 21, 22, 26, 28, 33, 34, 35, 38, 39, 44, 46, 51, 52, 55, 57, 58, 62, 65, 68, 69, 74, 76, 77, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 99, 104, 106, 111, 115, 116, 117, 118, 119, 122, 123, 124, 129, 133, 134, 136, 141, 142, 143, 145, 146, 148, 152, 153
Offset: 1
Keywords
Examples
20 is in the sequence because it has 2 distinct prime factors (2 and 5) and 5 > sqrt(20).
Programs
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Maple
with(numtheory): a:=proc(n) if nops(factorset(n))=2 and factorset(n)[2]^2>=n then n else fi end: seq(a(n),n=1..170);
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Mathematica
tdpfQ[n_]:=Module[{fi=FactorInteger[n]},Length[fi]==2&&fi[[2,1]]>Sqrt[n]]; Select[Range[ 200],tdpfQ] (* Harvey P. Dale, Aug 07 2023 *)