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A119973
Numbers of the form (4k+1)*2^j which are not a sum of two squares.
3
21, 33, 42, 57, 66, 69, 77, 84, 93, 105, 114, 129, 132, 133, 138, 141, 154, 161, 165, 168, 177, 186, 189, 201, 209, 210, 213, 217, 228, 237, 249, 253, 258, 264, 266, 273, 276, 282, 285, 297, 301, 308, 309, 321, 322, 329, 330, 336, 341, 345, 354, 357, 372
OFFSET
1,1
COMMENTS
Intersection of A091072 and A022544. - Robert Israel, Oct 28 2018
LINKS
EXAMPLE
42 is there because it's (4*5+1)*2^1 and is not a sum of two squares.
MAPLE
filter:= proc(n) local w; w:= n/2^padic:-ordp(n, 2);
w mod 4 = 1 and select(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(w)[2]) <> []
end proc:
select(filter, [$1..1000]); # Robert Israel, Oct 28 2018
MATHEMATICA
okQ[n_] := EvenQ[(n/2^IntegerExponent[n, 2]-1)/2] && SquaresR[2, n] == 0;
Select[Range[1000], okQ] (* Jean-François Alcover, Feb 09 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, Jun 03 2006
EXTENSIONS
More terms from Don Reble, Jul 24 2006
STATUS
approved