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 A078458 Total number of factors in a factorization of n into Gaussian primes. 15
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n)+1 is also the total number of factors in a factorization of n+n*i into Gaussian primes. - Jason Kimberley, Dec 17 2011 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Eric W. Weisstein, MathWorld: Gaussian Prime FORMULA 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, 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, Jul 14 2003 EXAMPLE 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, Jan 20 2003 MATHEMATICA Join[{0}, Table[f = FactorInteger[n, GaussianIntegers -> True]; cnt = Total[Transpose[f][]]; If[MemberQ[{-1, I, -I}, f[[1, 1]]], cnt--]; cnt, {n, 2, 100}]] (* T. D. Noe, Mar 31 2014 *) PROG (PARI) a(n)=my(f=factor(n)); sum(i=1, #f~, if(f[i, 1]%4==3, 1, 2)*f[i, 2]) \\ Charles R Greathouse IV, Mar 31 2014 CROSSREFS Cf. A078908-A078911, A007814, A065339, A083025, A086275 (number of distinct Gaussian primes in the factorization of n). Cf. A239626, A239627 (including units). Sequence in context: A130584 A339046 A265911 * A033317 A183200 A326732 Adjacent sequences:  A078455 A078456 A078457 * A078459 A078460 A078461 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 11 2003 EXTENSIONS More terms from Vladeta Jovovic, Jan 12 2003 STATUS approved

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Last modified May 23 04:06 EDT 2022. Contains 353959 sequences. (Running on oeis4.)