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

Author

Luis H. Gallardo, May 26 2011

Keywords

• nonn
• easy

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

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Subsequence of A191217.

Cf. A228058, A324898 (subsequences).

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

Programs

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 *)

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