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 A078909 Let r+i*s be the sum, with multiplicity, of the first-quadrant Gaussian primes dividing n; sequence gives s values. 6

%I

%S 0,2,0,4,3,2,0,6,0,5,0,4,5,2,3,8,5,2,0,7,0,2,0,6,6,7,0,4,7,5,0,10,0,7,

%T 3,4,7,2,5,9,9,2,0,4,3,2,0,8,0,8,5,9,9,2,3,6,0,9,0,7,11,2,0,12,8,2,0,

%U 9,0,5,0,6,11,9,6,4,0,7,0,11,0,11,0,4,8,2,7,6,13,5,5,4,0,2,3,10,13,2,0

%N Let r+i*s be the sum, with multiplicity, of the first-quadrant Gaussian primes 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 The sequence is fully additive.

%H Amiram Eldar, <a href="/A078909/b078909.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]]; Im[Plus @@ ((If[Abs[#] == 1, 0, #]& /@ p) * e)]]; Array[a, 100] (* _Amiram Eldar_, Feb 28 2020 *)

%Y Cf. A078458, A078908, A078910, A078911, A080088, A080089.

%K nonn,easy

%O 1,2

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

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

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Last modified August 6 19:52 EDT 2020. Contains 336256 sequences. (Running on oeis4.)