A034019 -id:A034019 - cp's OEIS frontend

A045897 Has both a primitive and imprimitive representation as x^2 + xy + y^2.

49, 147, 169, 343, 361, 507, 637, 931, 961, 1029, 1083, 1183, 1369, 1519, 1813, 1849, 1911, 2107, 2197, 2401, 2527, 2793, 2883, 2989, 3211, 3283, 3549, 3577, 3721, 3871, 4107, 4459, 4489, 4557, 4693, 4753, 5047, 5239, 5329, 5341, 5439, 5547, 6223, 6241

Offset: 1

N. J. A. Sloane

nonn

			49 = 7^2 = 5^2 + 5*3 + 3^2.

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Index entries for sequences related to A2 = hexagonal = triangular lattice

Intersection of A034017 and A034019.

Cf. A004611, A003136.

is(n)=my(f=factor(n), t); for(i=1, #f~, if(f[i, 1]%3!=1 && (f[i, 1]!=3 || f[i, 2]>1), return(0)); 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 \\ Charles R Greathouse IV, Nov 04 2015

Extended by Ray Chandler, Jan 29 2009

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

Original entry on oeis.org

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

N. J. A. Sloane

nonn

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

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

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.

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

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

cp's OEIS Frontend

A045897 Has both a primitive and imprimitive representation as x^2 + xy + y^2.

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