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A271184
Löschian numbers (A003136) of the form k^2+1.
1
1, 37, 325, 577, 1297, 2917, 3601, 4357, 7057, 8101, 9217, 14401, 15877, 22501, 24337, 28225, 32401, 41617, 44101, 46657, 57601, 60517, 69697, 72901, 79525, 86437, 90001, 93637, 108901, 133957, 147457, 156817, 176401, 197137, 202501, 219025, 224677, 236197, 291601, 298117, 318097
OFFSET
1,2
COMMENTS
Intersection of A002522 and A003136.
Corresponding values of k are 0, 6, 18, 24, 36, 54, 60, 66, 84, 90, 96, 120, 126, 150, 156, 168, 180, 204, 210, 216, 240, 246, 264, 270, 282, 294, 300, 306, ...
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
EXAMPLE
37 is a term because 37 = 6^2 + 1 = 4^2 + 4*3 + 3^2.
MATHEMATICA
Select[Range[10^6], And[IntegerQ@Sqrt[# - 1], 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, 2000, if(is(n=k^2+1), print1(n, ", ")));
CROSSREFS
Sequence in context: A114785 A061014 A130450 * A217117 A291859 A133554
KEYWORD
nonn
AUTHOR
Altug Alkan, Apr 01 2016
STATUS
approved