%I #26 Feb 16 2022 23:10:44

%S 5,13,17,29,37,41,45,53,61,73,89,97,101,109,113,117,137,149,153,157,

%T 173,181,193,197,229,233,241,245,257,261,269,277,281,293,313,317,325,

%U 333,337,349,353,369,373,389,397,401,405,409,421,425,433,449,457,461,477

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

%C 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.

%C See A228058 for the terms where m > 1. - _Antti Karttunen_, Apr 22 2019

%H Antti Karttunen, <a href="/A191218/b191218.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

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

%p with(numtheory): genodd := proc(b) local n,s,d; for n from 1 to b by 2 do s := sigma(n);

%p if modp(s,4)=2 then print(n); fi; od; end;

%t Select[Range[1,501,2],Mod[DivisorSigma[1,#],4]==2&] (* _Harvey P. Dale_, Nov 12 2017 *)

%o (PARI) forstep(n=1,10^3,2,if(2==(sigma(n)%4),print1(n,", "))) \\ _Joerg Arndt_, May 27 2011

%o (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

%Y Subsequence of A191217.

%Y Cf. A228058, A324898 (subsequences).

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

%K nonn,easy

%O 1,1

%A _Luis H. Gallardo_, May 26 2011