A034022 Numbers that are primitively or imprimitively represented by x^2+xy+y^2, but not both.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

a(n) = A198772(n) for n <= 32. - Reinhard Zumkeller, Oct 30 2011

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003136, A045611, A045897.

Symmetric difference of A034017 and A034019.

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

Programs

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
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
is(n)=my(f=factor(n)); prim(f)+imprim(f)==1 \\ Charles R Greathouse IV, Nov 04 2015

Extensions

Extended by Ray Chandler, Jan 29 2009

Data section further extended up to a(71), to better differentiate from nearby sequences, by Antti Karttunen, Jul 04 2024