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A098961 Sums of two squares and divisible by 13. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
a(n) = 13 * A001481(n+1) for n >= 1. - Joerg Arndt, Dec 03 2022
EXAMPLE
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 *
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 *)
CROSSREFS
Intersection of A001481 and A008595.
Cf. A094447.
Sequence in context: A044838 A033010 A019551 * A033897 A005029 A251149
KEYWORD
nonn
AUTHOR
Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Oct 22 2004
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)