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Numbers of the form prime(x)*prime(y) where x and y are relatively prime.
18

%I #41 Jan 04 2021 12:12:31

%S 4,6,10,14,15,22,26,33,34,35,38,46,51,55,58,62,69,74,77,82,85,86,93,

%T 94,95,106,118,119,122,123,134,141,142,143,145,146,155,158,161,166,

%U 177,178,187,194,201,202,205,206,209,214,215,217,218,219,221,226,249

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

%H Andrew Howroyd, <a href="/A300912/b300912.txt">Table of n, a(n) for n = 1..10000</a>

%e The sequence of all relatively prime pairs (columns) begins:

%e 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

%e 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

%t Select[Range[100],And[PrimeOmega[#]==2,GCD@@PrimePi/@If[#==1,{},FactorInteger[#]][[All,1]]==1]&]

%t 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 *)

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

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

%K nonn

%O 1,1

%A _Gus Wiseman_, Sep 06 2018