A191218 Odd numbers n such that sigma(n) is congruent to 2 modulo 4.

5, 13, 17, 29, 37, 41, 45, 53, 61, 73, 89, 97, 101, 109, 113, 117, 137, 149, 153, 157, 173, 181, 193, 197, 229, 233, 241, 245, 257, 261, 269, 277, 281, 293, 313, 317, 325, 333, 337, 349, 353, 369, 373, 389, 397, 401, 405, 409, 421, 425, 433, 449, 457, 461, 477

Offset

1,1

Comments

Exactly the numbers of the form p^{4k+1}*m^2 with p a prime congruent to 1 modulo 4 and m a positive integer coprime with p. The odd perfect numbers are all of this form.

See A228058 for the terms where m > 1. - Antti Karttunen, Apr 22 2019

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Example

For n=3 one has a(3)=17 since sigma(17) = 18 = 4*4 +2 is congruent to 2 modulo 4

Maple

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

Mathematica

Select[Range[1, 501, 2], Mod[DivisorSigma[1, #], 4]==2&] (* Harvey P. Dale, Nov 12 2017 *)

Prog

(PARI) forstep(n=1, 10^3, 2, if(2==(sigma(n)%4), print1(n, ", "))) \\ Joerg Arndt, May 27 2011
(PARI) list(lim)=my(v=List()); forstep(e=1, logint(lim\=1, 5), 4, forprimestep(p=5, sqrtnint(lim, e), 4, my(pe=p^e); forstep(m=1, sqrtint(lim\pe), 2, if(m%p, listput(v, pe*m^2))))); Set(v) \\ Charles R Greathouse IV, Feb 16 2022

Crossrefs

Subsequence of A191217.

Cf. A228058, A324898 (subsequences).

Cf. A000203, A191219, A324647, A324718, A324719.

Sequence in context: A208853 A265889 A359151 * A279857 A077426 A231754

Adjacent sequences: A191215 A191216 A191217 * A191219 A191220 A191221

Keyword

nonn,easy

Author

Luis H. Gallardo, May 26 2011

Status

approved