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A086275
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Number of distinct Gaussian primes in the factorization of n.
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1
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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; internal format)
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OFFSET
| 1,5
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COMMENTS
| 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).
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LINKS
| Eric Weisstein's World of Mathematics, Gaussian Prime
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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 (FrankTAW(AT)Netscape.net), Oct 18 2006
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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 4k+1 and 3 primes of the form 4k+3.
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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}]]
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CROSSREFS
| Cf. A005089, A005091, A059841, A078458 (number of Gaussian primes, with multiplicity).
Sequence in context: A085685 A112465 A112468 * A066855 A175685 A182591
Adjacent sequences: A086272 A086273 A086274 * A086276 A086277 A086278
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KEYWORD
| easy,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Jul 14 2003
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