A191217 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

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

EXAMPLE

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

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;

PROG

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

CROSSREFS

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

Cf. A191218, A228058, A332226 for other subsequences.