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%I #48 Aug 22 2022 14:24:55
%S 2,5,6,8,10,11,14,15,17,18,20,22,23,24,26,29,30,32,33,34,35,38,40,41,
%T 42,44,45,46,47,50,51,53,54,55,56,58,59,60,62,65,66,68,69,70,71,72,74,
%U 77,78,80,82,83,85,86,87,88,89,90,92,94,95,96,98,99,101,102,104,105
%N Not of the form x^2 + x*y + y^2.
%C Appears to be the sequence of nonsquare n such that sigma(n)==0 (mod 3). - _Benoit Cloitre_, Sep 17 2002
%C First counterexample is 147 = 11^2 + 11*2 + 2^2 since sigma(147) = 3 * 76. See A087943. - _Charles R Greathouse IV_, Jun 29 2011
%C Numbers n such that n-th coefficient of eta(x)^3/eta(x^3) is zero where eta(x) coefficients are given by A010815. - _Benoit Cloitre_, Oct 06 2005
%C A088534(a(n)) = 0. - _Reinhard Zumkeller_, Oct 30 2011
%H Reinhard Zumkeller, <a href="/A034020/b034020.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) ~ n. - _Charles R Greathouse IV_, Jul 05 2017
%t Select[Range@ 105, ! Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]] &] (* _Michael De Vlieger_, Jan 06 2016 *)
%o (PARI) default(seriesprecision, 105); for(n=1, 105, if (polcoeff(eta(x)^3/eta(x^3)+O(x^(n+1)), n) == 0, print1(n,","))) \\ _Benoit Cloitre_, Oct 06 2005
%o (PARI) x='x+O('x^100); p=eta(x)^3/eta(x^3); for(n=1, 99, if(polcoeff(p, n)==0, print1(n, ", "))); \\ _Altug Alkan_, Nov 08 2015
%o (PARI) list(lim)=my(v=List(), y, t); lim\=1; for(x=0, sqrtint(lim\3), my(y=x, t); while((t=x^2+x*y+y^2)<=lim, listput(v, t); y++)); v=Set(v); setminus([2..lim], v) \\ _Charles R Greathouse IV_, Jul 05 2017
%o (Haskell)
%o a034020 n = a034020_list !! (n-1)
%o a034020_list = f [0..] a003136_list where
%o f (x:xs) ys'@(y:ys) | x < y = x : f xs ys'
%o | otherwise = f xs ys
%o -- _Reinhard Zumkeller_, Oct 30 2011
%Y Cf. A003136 (complement), A003627 (primes). Subsequence of A087943.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E More terms from _James A. Sellers_, May 04 2000
%E Correct offset=1 by _Ray Chandler_, Jan 29 2009
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