A119973 - OEIS

%I #15 Feb 09 2023 05:01:23

%S 21,33,42,57,66,69,77,84,93,105,114,129,132,133,138,141,154,161,165,

%T 168,177,186,189,201,209,210,213,217,228,237,249,253,258,264,266,273,

%U 276,282,285,297,301,308,309,321,322,329,330,336,341,345,354,357,372

%N Numbers of the form (4k+1)*2^j which are not a sum of two squares.

%C Intersection of A091072 and A022544. - _Robert Israel_, Oct 28 2018

%H Robert Israel, <a href="/A119973/b119973.txt">Table of n, a(n) for n = 1..10000</a>

%e 42 is there because it's (4*5+1)*2^1 and is not a sum of two squares.

%p filter:= proc(n) local w; w:= n/2^padic:-ordp(n,2);

%p w mod 4 = 1 and select(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(w)[2]) <> []

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, Oct 28 2018

%t okQ[n_] := EvenQ[(n/2^IntegerExponent[n, 2]-1)/2] && SquaresR[2, n] == 0;

%t Select[Range[1000], okQ] (* _Jean-François Alcover_, Feb 09 2023 *)

%Y Cf. A001481, A022544, A084109, A091072, A120772.

%K easy,nonn

%O 1,1

%A _Alford Arnold_, Jun 03 2006

%E More terms from _Don Reble_, Jul 24 2006