A115956 Numbers n having exactly 2 distinct prime factors, the largest of which is greater than or equal to sqrt(n) (i.e., sqrt(n)-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

1,1

Links

Table of n, a(n) for n=1..62.

Example

20 is in the sequence because it has 2 distinct prime factors (2 and 5) and 5 > sqrt(20).

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);

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 *)

Crossrefs

Cf. A115957, A115958, A115959, A115960, A115961.

Sequence in context: A359870 A376158 A063763 * A066073 A339438 A268376

Adjacent sequences: A115953 A115954 A115955 * A115957 A115958 A115959

Keyword

nonn

Author

Emeric Deutsch, Feb 02 2006

Status

approved