A271185 Löschian numbers (A003136) of the form k^3+1.

1, 9, 28, 217, 513, 1332, 1729, 3376, 5833, 8001, 13825, 17577, 19684, 27001, 42876, 46657, 54873, 74089, 103824, 110593, 132652, 175617, 216001, 238329, 250048, 287497, 373249, 405225, 421876, 474553, 512001, 571788, 729001, 778689, 884737, 970300, 1061209, 1225044, 1259713, 1331001

Offset

1,2

Comments

Intersection A001093 and A003136.

Corresponding values of k are 0, 2, 3, 6, 8, 11, 12, 15, 18, 20, 24, 26, 27, 30, 35, 36, 38, 42, 47, 48, 51, 56, 60, 62, 63, 66, 72, 74, 75, 78, 80, 83, 90, ...

Links

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

Example

28 is a term because 28 = 3^3 + 1 = 2^2 + 2*4 + 4^2.

Mathematica

Select[Range[10^6], And[IntegerQ@ Power[# - 1, 1/3], Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]]] &] (* Michael De Vlieger, Apr 01 2016 *)

Prog

(PARI) is(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
for(k=0, 1e3, if(is(n=k^3+1), print1(n, ", ")));

Crossrefs

Cf. A001093, A003136.

Sequence in context: A073706 A226976 A042501 * A306843 A277511 A041154

Adjacent sequences: A271182 A271183 A271184 * A271186 A271187 A271188

Keyword

nonn

Author

Altug Alkan, Apr 01 2016

Status

approved