%I #14 Feb 28 2020 08:39:57

%S 0,2,3,4,3,5,7,6,6,5,11,7,5,9,6,8,5,8,19,7,10,13,23,9,6,7,9,11,7,8,31,

%T 10,14,7,10,10,7,21,8,9,9,12,43,15,9,25,47,11,14,8,8,9,9,11,14,13,22,

%U 9,59,10,11,33,13,12,8,16,67,9,26,12,71,12,11,9,9,23,18,10,79,11,12,11

%N Let r+i*s be the sum, with multiplicity, of the first-quadrant Gaussian primes dividing n; sequence gives r values (with a(1) = 0).

%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 The sequence is fully additive.

%H Amiram Eldar, <a href="/A078908/b078908.txt">Table of n, a(n) for n = 1..10000</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 5 factors into the product of the primes 1+2*i, 1-2*i, but the first-quadrant associate of 1-2*i is i*(1-2*i) = 2+i, so r+i*s = 1+2*i + 2+i = 3+3*i. Therefore a(5) = 3.

%t a[n_] := Module[{f = FactorInteger[n, GaussianIntegers->True]}, p = f[[;;,1]]; e = f[[;;,2]]; Re[Plus @@ ((If[Abs[#] == 1, 0, #]& /@ p) * e)]]; Array[a, 100] (* _Amiram Eldar_, Feb 28 2020 *)

%Y Cf. A078458, A078909, A078910, A078911, A080088, A080089.

%K nonn,easy

%O 1,2

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

%E More terms and information from _Vladeta Jovovic_, Jan 27 2003