1,2

Michael Somos, PARI program for finding prime decomposition of Gaussian integers

Index entries for Gaussian integers and primes

Eric Weisstein's World of Mathematics, Gaussian Prime

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.yu), Jan 20 2003

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

2 = (1+i)*(1-i), so a(2) = 2; 9 = 3*3, so a(9) = 2.

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.yu), Jan 20 2003

Cf. A078908-A078911.

Cf. A007814, A065339, A083025, A086275 (number of distinct Gaussian primes in the factorization of n).

Adjacent sequences: A078455 A078456 A078457 this_sequence A078459 A078460 A078461

Sequence in context: A094571 A104733 A130584 this_sequence A033317 A007733 A128520

nonn,easy

njas, Jan 11 2003

More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Jan 12 2003