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

1,3

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

Prog

(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

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.

Sequence in context: A035238 A003136 A326421 * A329963 A198772 A185256

Adjacent sequences: A034019 A034020 A034021 * A034023 A034024 A034025

Keyword

nonn

Author

N. J. A. Sloane.

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

Status

approved