A300912 Numbers of the form prime(x)*prime(y) where x and y are relatively prime.

4, 6, 10, 14, 15, 22, 26, 33, 34, 35, 38, 46, 51, 55, 58, 62, 69, 74, 77, 82, 85, 86, 93, 94, 95, 106, 118, 119, 122, 123, 134, 141, 142, 143, 145, 146, 155, 158, 161, 166, 177, 178, 187, 194, 201, 202, 205, 206, 209, 214, 215, 217, 218, 219, 221, 226, 249

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Example

The sequence of all relatively prime pairs (columns) begins:
  1  1  1  1  2  1  1  2  1  3  1  1  2  3  1  1  2  1  4  1  3  1  2  1  3
  1  2  3  4  3  5  6  5  7  4  8  9  7  5 10 11  9 12  5 13  7 14 11 15  8

Mathematica

Select[Range[100], And[PrimeOmega[#]==2, GCD@@PrimePi/@If[#==1, {}, FactorInteger[#]][[All, 1]]==1]&]
With[{nn=40}, Join[{4}, Take[Prime[#[[1]]]Prime[#[[2]]]&/@Select[Subsets[ Range[ nn], {2}], CoprimeQ@@#&]//Union, Floor[Prime[nn]/2]]]] (* Harvey P. Dale, Jan 04 2021 *)

Prog

(PARI) ok(n)={my(f=factor(n)); bigomega(f)==2 && gcd(apply(primepi, f[, 1]))==1} \\ Andrew Howroyd, Oct 26 2018

Crossrefs

Cf. A001358, A000837, A001221, A001222, A006881, A289508, A289509, A318990.

Sequence in context: A065073 A359157 A084997 * A175706 A110507 A224467

Adjacent sequences: A300909 A300910 A300911 * A300913 A300914 A300915

Keyword

nonn

Author

Gus Wiseman, Sep 06 2018

Status

approved