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
KEYWORD
nonn
AUTHOR
Luis H. Gallardo, May 26 2011
STATUS
approved