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

1,1

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.

Links

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

Example

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

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 *)

Crossrefs

Sequence in context: A118837 A117828 A117830 * A061516 A146135 A101116

Adjacent sequences: A191216 A191217 A191218 * A191220 A191221 A191222

Keyword

nonn

Author

Luis H. Gallardo, May 26 2011

Status

approved