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Positive integers k such that n=k*(2*k-1) satisfies: sigma(n) congruent to 2 modulo 4.
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%I #13 Sep 30 2018 13:47:03

%S 5,9,13,41,49,61,113,121,169,181,225,289,313,421,441,613,625,761,925,

%T 1013,1201,1301,1521,1681,1741,1849,1861,2025,2113,2381,2401,2521,

%U 3121,3481,3613,3969,4325,4513,4761,4901

%N Positive integers k such that n=k*(2*k-1) satisfies: sigma(n) congruent to 2 modulo 4.

%C If there are odd perfect numbers n of the form n=k*(2*k-1) the corresponding k should appear in this sequence. The sequence has no even terms.

%H Harvey P. Dale, <a href="/A191219/b191219.txt">Table of n, a(n) for n = 1..700</a>

%e For n=4, a(4) = 41 since n = 41*(82 -1) = 3321 and sigma(3321)= 5082 = 4*1270 +2.

%p with(numtheory): genz := proc(b)local z,n,s,d; for z from 1 to b by 2 do n := z*(2*z-1); s := sigma(n); if modp(n,4)=2 then print(z); fi; od; end;

%t Select[Range[1,5001,2],Mod[DivisorSigma[1,#(2#-1)],4]==2&] (* _Harvey P. Dale_, Sep 30 2018 *)

%K nonn

%O 1,1

%A _Luis H. Gallardo_, May 26 2011