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 A086275 Number of distinct Gaussian primes in the factorization of n. 11
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS As shown in the formula, a(n) depends on the number of distinct primes of the forms 4*k+1 (A005089) and 4*k-1 (A005091) and whether n is divisible by 2 (A059841). Note that associated divisors are counted only once. - Jianing Song, Aug 30 2018 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Eric W. Weisstein, MathWorld: Gaussian Prime FORMULA a(n) = A059841(n) + 2*A005089(n) + A005091(n). Additive with a(p^e) = 2 if p = 1 (mod 4), 1 otherwise. - Franklin T. Adams-Watters, Oct 18 2006 EXAMPLE 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 4*k+1 and 3 primes of the form 4*k+3. Over the Gaussian integers, 1006655265000 is factored as i*(1 + i)^6*(2 + i)^4*(2 - i)^4*3^2*7^5*11^3, the 6 distinct Gaussian factors are 1 + i, 2 + i, 2 - i, 3, 7 and 11. MATHEMATICA Join[{0}, Table[f=FactorInteger[n, GaussianIntegers->True]; cnt=Length[f]; If[MemberQ[{-1, I, -I}, f[[1, 1]]], cnt-- ]; cnt, {n, 2, 100}]] PROG (PARI) a(n)=my(f=factor(n)[, 1]); sum(i=1, #f, if(f[i]%4==1, 2, 1)) \\ Charles R Greathouse IV, Sep 14 2015 CROSSREFS Cf. A005089, A005091, A059841, A078458 (number of Gaussian primes, with multiplicity). Sequence in context: A112465 A112468 A207194 * A066855 A175685 A331182 Adjacent sequences:  A086272 A086273 A086274 * A086276 A086277 A086278 KEYWORD easy,nonn AUTHOR T. D. Noe, Jul 14 2003 STATUS approved

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Last modified January 22 19:52 EST 2020. Contains 331153 sequences. (Running on oeis4.)