A071011 Numbers n such that n is a sum of 2 squares (i.e., n is in A001481(k)) and sigma(n) == 0 (mod 4).

65, 85, 125, 130, 145, 170, 185, 205, 221, 250, 260, 265, 290, 305, 340, 365, 370, 377, 410, 442, 445, 481, 485, 493, 500, 505, 520, 530, 533, 545, 565, 580, 585, 610, 629, 680, 685, 689, 697, 730, 740, 745, 754, 765, 785, 793, 820, 865, 884, 890, 901, 905

Offset

1,1

Comments

It is conjectured that if m is not a sum of 2 squares (i.e., m is in A022544(k)) sigma(m) == 0 (mod 4).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[10^3], And[SquaresR[2, #] > 0, Divisible[DivisorSigma[1, #], 4]] &] (* Michael De Vlieger, Jul 30 2017 *)

Prog

(PARI) for(n=1, 1000, if(1-sign(sum(i=0, n, sum(j=0, i, if(i^2+j^2-n, 0, 1))))+sigma(n)%4==0, print1(n, ", ")))
(Python)
from math import prod
from itertools import count, islice
from sympy import factorint
def A071011_gen(): # generator of terms
    return filter(lambda n:(lambda f:all(p & 3 != 3 or e & 1 == 0 for p, e in f) and prod((p**(e+1)-1)//(p-1) & 3 for p, e in f) & 3 == 0)(factorint(n).items()), count(0))
A071011_list = list(islice(A071011_gen(), 30)) # Chai Wah Wu, Jun 27 2022

Crossrefs

Cf. A001481, A022544.

Sequence in context: A025312 A024508 A025303 * A165158 A084648 A224770

Adjacent sequences: A071008 A071009 A071010 * A071012 A071013 A071014

Keyword

easy,nonn

Author

Benoit Cloitre, May 19 2002

Status

approved