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A191218
Odd numbers n such that sigma(n) is congruent to 2 modulo 4.
26
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
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).
Sequence in context: A208853 A265889 A359151 * A279857 A077426 A231754
KEYWORD
nonn,easy
AUTHOR
Luis H. Gallardo, May 26 2011
STATUS
approved