A034020 Not of the form x^2 + x*y + y^2.

2, 5, 6, 8, 10, 11, 14, 15, 17, 18, 20, 22, 23, 24, 26, 29, 30, 32, 33, 34, 35, 38, 40, 41, 42, 44, 45, 46, 47, 50, 51, 53, 54, 55, 56, 58, 59, 60, 62, 65, 66, 68, 69, 70, 71, 72, 74, 77, 78, 80, 82, 83, 85, 86, 87, 88, 89, 90, 92, 94, 95, 96, 98, 99, 101, 102, 104, 105

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

Appears to be the sequence of nonsquare n such that sigma(n)==0 (mod 3). - Benoit Cloitre, Sep 17 2002

First counterexample is 147 = 11^2 + 11*2 + 2^2 since sigma(147) = 3 * 76. See A087943. - Charles R Greathouse IV, Jun 29 2011

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

A088534(a(n)) = 0. - Reinhard Zumkeller, Oct 30 2011

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003136 (complement), A003627 (primes). Subsequence of A087943.

Programs

Haskell

a034020 n = a034020_list !! (n-1)
a034020_list = f [0..] a003136_list where
   f (x:xs) ys'@(y:ys) | x < y = x : f xs ys'
                       | otherwise = f xs ys
-- Reinhard Zumkeller, Oct 30 2011

Mathematica

Select[Range@ 105, ! Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]] &] (* Michael De Vlieger, Jan 06 2016 *)

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

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

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

Formula

a(n) ~ n. - Charles R Greathouse IV, Jul 05 2017

Extensions

More terms from James Sellers, May 04 2000

Correct offset=1 by Ray Chandler, Jan 29 2009