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A078911 Let r+i*s be the sum of the distinct first-quadrant Gaussian integers dividing n; sequence gives s values. 7

%I

%S 0,1,0,3,3,4,0,7,0,19,0,12,5,8,12,15,5,13,0,51,0,12,0,28,25,35,0,24,7,

%T 76,0,31,0,41,24,39,7,20,20,115,9,32,0,36,39,24,0,60,0,138,20,95,9,40,

%U 36,56,0,61,0,204,11,32,0,63,92,48,0,113,0,152,0,91,11,71,100,60,0,140

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

%C a(A004614(n)) = 0; a(n) = A078910(n)-A000203(n). - _Vladeta Jovovic_, Jan 11 2003

%H M. F. Hasler, <a href="/A078911/b078911.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>

%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) = 3.

%t Table[Im[Plus@@Divisors[n, GaussianIntegers -> True]], {n, 65}] (* _Alonso del Arte_, Jan 24 2012; typo fixed by _Virgile Andreani_, Jul 10 2016 *)

%o (PARI) A078911(n,S=[])=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. A078910, A078458, A078908, A078909, A078930.

%K nonn,easy

%O 1,4

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

%E More terms from _Vladeta Jovovic_, Jan 11 2003

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Last modified April 23 14:15 EDT 2019. Contains 322386 sequences. (Running on oeis4.)