A098961 - OEIS

%I #13 Dec 03 2022 23:05:47

%S 13,26,52,65,104,117,130,169,208,221,234,260,325,338,377,416,442,468,

%T 481,520,533,585,637,650,676,689,754,793,832,845,884,936,949,962,1040,

%U 1053,1066,1105,1157,1170,1261,1274,1300,1313

%N Sums of two squares and divisible by 13.

%H Robert Israel, <a href="/A098961/b098961.txt">Table of n, a(n) for n = 1..10000</a>

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

%e Sums not divisible by 13 are shown in asterisks:

%e .

%e       |   1    4    9   16   25   36   49   64   81  100  121

%e   ----+------------------------------------------------------

%e     1 |   *    *    *    *   26    *    *   65    *    *    *

%e     4 |   *    *   13    *    *    *    *    *    *  104    *

%e     9 |   *   13    *    *    *    *    *    *    *    *  130

%e    16 |   *    *    *    *    *   52   65    *    *    *    *

%e    25 |  26    *    *    *    *    *    *    *    *    *    *

%e    36 |   *    *    *   52    *    *    *    *  117    *    *

%e    49 |   *    *    *   65    *    *    *    *  130    *    *

%e    64 |  65    *    *    *    *    *    *    *    *    *    *

%e    81 |   *    *    *    *    *  117  130    *    *    *    *

%e   100 |   *  104    *    *    *    *    *    *    *    *  221

%e   121 |   *    *  130    *    *    *    *    *    *  221    *

%p filter:= proc(n) local t,F;

%p   F:= select(t -> t[2]::odd, ifactors(n)[2]);

%p   andmap(t -> t[1] = 2 or t[1] mod 4 = 1, F);

%p end proc:

%p select(filter, [seq(i,i=13..10000, 13)]); # _Robert Israel_, Dec 02 2022

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

%Y Intersection of A001481 and A008595.

%Y Cf. A094447.

%K nonn

%O 1,1

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