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

5, 10, 13, 17, 20, 26, 29, 34, 37, 40, 41, 45, 52, 53, 58, 61, 68, 73, 74, 80, 82, 89, 90, 97, 101, 104, 106, 109, 113, 116, 117, 122, 136, 137, 146, 148, 149, 153, 157, 160, 164, 173, 178, 180, 181, 193, 194, 197, 202, 208, 212, 218, 226, 229, 232, 233, 234, 241, 244, 245, 257, 261, 269

Offset: 1

Author

Luis H. Gallardo, May 26 2011

Keywords

• nonn

Comments

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.

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

Examples

			For n=2, a(2) = 10 since sigma(10) = 18 = 4*4 + 2 is congruent to 2 modulo 4
		

Links

• Ray Chandler, Table of n, a(n) for n = 1..10000

Crossrefs

Similar to, but different from, A230779, which is a subsequence.

Cf. A191218, A228058, A332226 for other subsequences.

Cf. A353812 (characteristic function).

Programs

Maple

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

PARI

for(n=1,10^3,if(2==(sigma(n)%4),print1(n,", "))) /* Joerg Arndt, May 27 2011 */