cp's OEIS Frontend

A191217 Numbers n such that sigma(n) is congruent to 2 modulo 4.

%I A191217 #32 Jun 02 2025 04:07:30
%S A191217 5,10,13,17,20,26,29,34,37,40,41,45,52,53,58,61,68,73,74,80,82,89,90,
%T A191217 97,101,104,106,109,113,116,117,122,136,137,146,148,149,153,157,160,
%U A191217 164,173,178,180,181,193,194,197,202,208,212,218,226,229,232,233,234,241,244,245,257,261,269
%N A191217 Numbers n such that sigma(n) is congruent to 2 modulo 4.
%C A191217 These numbers are exactly the numbers of the form 2^a * p^(4b+1) * m^2 where p is a prime number congruent to 1 modulo 4, a is a nonnegative integer, and m is a positive integer coprime to p. In particular, they are also sums of two squares: the sequence has the first 12 terms in common with A132777.
%C A191217 I corrected the above comment by adding the exponent (4b+1) to p, because otherwise it would miss terms like a(614) = 3125 = 5^5, a(1140) = 6250 = 2 * 5^5, a(4421) = 28125 = 5^5 * 3^2, etc. - _Antti Karttunen_, May 25 2022
%H A191217 Ray Chandler, <a href="/A191217/b191217.txt">Table of n, a(n) for n = 1..10000</a>
%e A191217 For n=2, a(2) = 10 since sigma(10) = 18 = 4*4 + 2 is congruent to 2 modulo 4
%p A191217 with(numtheory): gen := proc(b) local n,s,d; for n from 1 to b do s := sigma(n);
%p A191217 if modp(s,4)=2 then print(n); fi; od; end;
%o A191217 (PARI) for(n=1,10^3,if(2==(sigma(n)%4),print1(n,", "))) /* _Joerg Arndt_, May 27 2011 */
%Y A191217 Similar to, but different from, A230779, which is a subsequence.
%Y A191217 Cf. A191218, A228058, A332226 for other subsequences.
%Y A191217 Cf. A353812 (characteristic function).
%K A191217 nonn
%O A191217 1,1
%A A191217 _Luis H. Gallardo_, May 26 2011