A098961 Sums of two squares and divisible by 13.

13, 26, 52, 65, 104, 117, 130, 169, 208, 221, 234, 260, 325, 338, 377, 416, 442, 468, 481, 520, 533, 585, 637, 650, 676, 689, 754, 793, 832, 845, 884, 936, 949, 962, 1040, 1053, 1066, 1105, 1157, 1170, 1261, 1274, 1300, 1313

Offset: 1

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Oct 22 2004

Keywords

• nonn
• changed

Examples

			Sums not divisible by 13 are shown in asterisks:
.
      |   1    4    9   16   25   36   49   64   81  100  121
  ----+------------------------------------------------------
    1 |   *    *    *    *   26    *    *   65    *    *    *
    4 |   *    *   13    *    *    *    *    *    *  104    *
    9 |   *   13    *    *    *    *    *    *    *    *  130
   16 |   *    *    *    *    *   52   65    *    *    *    *
   25 |  26    *    *    *    *    *    *    *    *    *    *
   36 |   *    *    *   52    *    *    *    *  117    *    *
   49 |   *    *    *   65    *    *    *    *  130    *    *
   64 |  65    *    *    *    *    *    *    *    *    *    *
   81 |   *    *    *    *    *  117  130    *    *    *    *
  100 |   *  104    *    *    *    *    *    *    *    *  221
  121 |   *    *  130    *    *    *    *    *    *  221    *
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A001481 and A008595.

Cf. A094447.

Programs

Maple

filter:= proc(n) local t,F;
  F:= select(t -> t[2]::odd, ifactors(n)[2]);
  andmap(t -> t[1] = 2 or t[1] mod 4 = 1, F);
end proc:
select(filter, [seq(i,i=13..10000, 13)]); # Robert Israel, Dec 02 2022

Mathematica

With[{nn=50},Take[Union[Select[Total/@Subsets[Range[nn]^2,{2}], Divisible[ #,13]&]],nn]] (* Harvey P. Dale, Aug 15 2014 *)

Formula

a(n) = 13 * A001481(n+1) for n >= 1. - Joerg Arndt, Dec 03 2022