A191219 Positive integers k such that n=k*(2*k-1) satisfies: sigma(n) congruent to 2 modulo 4.

5, 9, 13, 41, 49, 61, 113, 121, 169, 181, 225, 289, 313, 421, 441, 613, 625, 761, 925, 1013, 1201, 1301, 1521, 1681, 1741, 1849, 1861, 2025, 2113, 2381, 2401, 2521, 3121, 3481, 3613, 3969, 4325, 4513, 4761, 4901

Offset: 1

Author

Luis H. Gallardo, May 26 2011

Keywords

• nonn

Comments

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.

Examples

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..700

Programs

Maple

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;

Mathematica

Select[Range[1,5001,2],Mod[DivisorSigma[1,#(2#-1)],4]==2&] (* Harvey P. Dale, Sep 30 2018 *)