%I A086275
%S A086275 0,1,1,1,2,2,1,1,1,3,1,2,2,2,3,1,2,2,1,3,2,2,1,2,2,3,1,2,2,4,1,1,2,3,3,
%T A086275 2,2,2,3,3,2,3,1,2,3,2,1,2,1,3,3,3,2,2,3,2,2,3,1,4,2,2,2,1,4,3,1,3,2,4,
%U A086275 1,2,2,3,3,2,2,4,1,3,1,3,1,3,4,2,3,2,2,4,3,2,2,2,3,2,2,2,2,3
%N A086275 Number of distinct Gaussian primes in the factorization of n.
%C A086275 As shown in the formula, a(n) depends on the number of distinct primes 
               of the forms 4k+1 (A005089) and 4k-1 (A005091) and whether n is divisible 
               by 2 (A059841).
%H A086275 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GaussianPrime.html">Gaussian Prime</a>
%F A086275 a(n) = A059841(n) + 2*A005089(n) + A005091(n)
%F A086275 Additive with a(p^e) = 2 if p = 1 (mod 4), 1 otherwise. - Franklin T. 
               Adams-Watters (FrankTAW(AT)Netscape.net), Oct 18 2006
%e A086275 a(1006655265000) = a(2^3 *3^2*5^4*7^5*11^3) = 1 + 2*1 + 3 = 6 because 
               n is divisible by 2, has 1 prime factor of the form 4k+1 and 3 primes 
               of the form 4k+3.
%t A086275 Join[{0}, Table[f=FactorInteger[n, GaussianIntegers->True]; cnt=Length[f]; 
               If[MemberQ[{-1, I, -I}, f[[1, 1]]], cnt-- ]; cnt, {n, 2, 100}]]
%Y A086275 Cf. A005089, A005091, A059841, A078458 (number of Gaussian primes, with 
               multiplicity).
%Y A086275 Sequence in context: A085685 A112465 A112468 this_sequence A066855 A058914 
               A123682
%Y A086275 Adjacent sequences: A086272 A086273 A086274 this_sequence A086276 A086277 
               A086278
%K A086275 easy,nonn
%O A086275 1,5
%A A086275 T. D. Noe (noe(AT)sspectra.com), Jul 14 2003