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Numbers that are divisible only by primes congruent to 2 mod 3.
10

%I #21 Sep 08 2022 08:44:33

%S 1,2,4,5,8,10,11,16,17,20,22,23,25,29,32,34,40,41,44,46,47,50,53,55,

%T 58,59,64,68,71,80,82,83,85,88,89,92,94,100,101,106,107,110,113,115,

%U 116,118,121,125,128,131,136,137

%N Numbers that are divisible only by primes congruent to 2 mod 3.

%C Square roots of numbers n such that n-th coefficient of eta(x)^3/eta(x^3)=-1, where eta(x) is given by A010815. - _Benoit Cloitre_, Oct 06 2005

%C Apparently the complement to A135412. - _R. J. Mathar_, Aug 21 2016

%H T. D. Noe, <a href="/A004612/b004612.txt">Table of n, a(n) for n = 1..10000</a>

%e 2=2, 4=2^2, 5=5, 8=2^3, 10=2*5, 11=11, 16=2^4, 17=17, 20=2^2*5, 22 = 2*11, 23=23, 25=5^2, 29=29... (products of powers of elements of A003627). - _R. J. Mathar_, Jan 22 2021

%t ok[1]=True;ok[n_]:=And@@(Mod[#,3]==2&)/@FactorInteger[n][[All,1]];Select[Range[200],ok] (* _Vincenzo Librandi_, Aug 21 2012 *)

%o (Magma) [n: n in [1..300] | forall{d: d in PrimeDivisors(n) | d mod 3 eq 2}]; // _Vincenzo Librandi_, Aug 21 2012

%Y Cf. A004611, A003627.

%K nonn

%O 1,2

%A _N. J. A. Sloane_