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Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values.
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%I #19 Jan 25 2021 10:26:56

%S 1,4,4,10,9,16,8,22,13,37,12,40,19,32,36,46,23,52,20,93,32,48,24,88,

%T 56,77,40,80,37,148,32,94,48,95,72,130,45,80,76,205,51,128,44,120,117,

%U 96,48,184,57,231,92,193,63,160,108,176,80,151,60,372,73,128,104,190,176

%N Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives r values.

%C A Gaussian integer z = x+iy is in the first quadrant if x > 0, y >= 0. Just one of the 4 associates z, -z, i*z, -i*z is in the first quadrant.

%H M. F. Hasler, <a href="/A078910/b078910.txt">Table of n, a(n) for n = 1..1000</a>.

%H Michael Somos, <a href="/A078458/a078458.txt">PARI program for finding prime decomposition of Gaussian integers</a>

%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>

%F a(n) = A078911(n)+A000203(n). - _Vladeta Jovovic_, Jan 11 2003

%e The distinct first-quadrant divisors of 4 are 1, 1+i, 2, 2+2*i, 4, with sum 10+3*i, so a(4) = 10.

%t Table[Re[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* _Alonso del Arte_, Jan 24 2012 *)

%o (PARI) A078910(n,S=[])=sigma(n)+sumdiv(n*I,d,if(real(d)&imag(d)&!setsearch(S,d=vecsort(abs([real(d),imag(d)]))),S=setunion(S,[d]);(d[1]+d[2])>>(d[1]==d[2]))) \\ _M. F. Hasler_, Nov 22 2007

%Y Cf. A000203, A078911, A078458, A078908, A078909, A078930.

%Y Cf. A062327 for the number of first quadrant divisors of n.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_, Jan 11 2003

%E More terms from _Vladeta Jovovic_, Jan 11 2003