Search: id:A078458
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%I A078458
%S A078458 0,2,1,4,2,3,1,6,2,4,1,5,2,3,3,8,2,4,1,6,2,3,1,7,4,4,3,5,2,5,1,10,2,4,
               3,
%T A078458 6,2,3,3,8,2,4,1,5,4,3,1,9,2,6,3,6,2,5,3,7,2,4,1,7,2,3,3,12,4,4,1,6,2,
               5,
%U A078458 1,8,2,4,5,5,2,5,1,10,4,4,1,6,4,3,3,7,2,6,3,5,2,3,3,11,2,4,3,8,2,5,1,8
%N A078458 Total number of factors in a factorization of n into Gaussian primes.
%H A078458 Michael Somos, <a href="a078458.txt">PARI program for finding prime decomposition 
               of Gaussian integers</a>
%H A078458 <a href="Sindx_Ga.html#gaussians">Index entries for Gaussian integers 
               and primes</a>
%H A078458 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               GaussianPrime.html">Gaussian Prime</a>
%F A078458 Fully additive with a(p)=2 if p=2 or p mod 4=1 and a(p)=1 if p mod 4=3. 
               - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 20 2003
%F A078458 a(n) depends on the number of primes of the forms 4k+1 (A083025) and 
               4k-1 (A065339) and on the highest power of 2 dividing n (A007814): 
               a(n) = 2*A007814(n) + 2*A083025(n) + A065339(n) - T. D. Noe (noe(AT)sspectra.com), 
               Jul 14 2003
%e A078458 2 = (1+i)*(1-i), so a(2) = 2; 9 = 3*3, so a(9) = 2.
%e A078458 a(1006655265000) = a(2^3*3^2*5^4*7^5*11^3) = 3*a(2)+2*a(3)+4*a(5)+5*a(7)+3*a(11) 
               = 3*2+2*1+4*2+5*1+3*1 = 24. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jan 20 2003
%Y A078458 Cf. A078908-A078911.
%Y A078458 Cf. A007814, A065339, A083025, A086275 (number of distinct Gaussian primes 
               in the factorization of n).
%Y A078458 Sequence in context: A104733 A153281 A130584 this_sequence A033317 A007733 
               A128520
%Y A078458 Adjacent sequences: A078455 A078456 A078457 this_sequence A078459 A078460 
               A078461
%K A078458 nonn,easy
%O A078458 1,2
%A A078458 N. J. A. Sloane (njas(AT)research.att.com), Jan 11 2003
%E A078458 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2003

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