A034022 - OEIS

%I #22 Jul 04 2024 09:21:09

%S 0,1,3,4,7,9,12,13,16,19,21,25,27,28,31,36,37,39,43,48,52,57,61,63,64,

%T 67,73,75,76,79,81,84,91,93,97,100,103,108,109,111,112,117,121,124,

%U 127,129,133,139,144,148,151,156,157,163,171,172,175,181,183,189,192,193,196,199,201,208,211,217,219,223,225

%N Numbers that are primitively or imprimitively represented by x^2+xy+y^2, but not both.

%C a(n) = A198772(n) for n <= 32. - _Reinhard Zumkeller_, Oct 30 2011

%H Charles R Greathouse IV, <a href="/A034022/b034022.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) prim(f)=for(i=1, #f~, if(f[i, 1]%3!=1 && (f[i, 1]!=3 || f[i, 2]>1), return(factorback(f)==0))); 1

%o imprim(f)=my(t); for(i=1, #f~, if(f[i, 1]%3<2 && f[i, 2]>1, t=1); if(f[i, 1]%3==2, if(f[i, 2]%2, return(0), t=1))); t

%o is(n)=my(f=factor(n)); prim(f)+imprim(f)==1 \\ _Charles R Greathouse IV_, Nov 04 2015

%Y Cf. A003136, A045611, A045897.

%Y Symmetric difference of A034017 and A034019.

%Y After the initial 0, differs from A329963 next time at a(63) = 196, term which is not present in the latter.

%K nonn

%O 1,3

%A _N. J. A. Sloane_.

%E Extended by _Ray Chandler_, Jan 29 2009

%E Data section further extended up to a(71), to better differentiate from nearby sequences, by _Antti Karttunen_, Jul 04 2024