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A062327
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Number of divisors of n over the Gaussian integers.
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4
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1, 3, 2, 5, 4, 6, 2, 7, 3, 12, 2, 10, 4, 6, 8, 9, 4, 9, 2, 20, 4, 6, 2, 14, 9, 12, 4, 10, 4, 24, 2, 11, 4, 12, 8, 15, 4, 6, 8, 28, 4, 12, 2, 10, 12, 6, 2, 18, 3, 27, 8, 20, 4, 12, 8, 14, 4, 12, 2, 40, 4, 6, 6, 13, 16, 12, 2, 20, 4, 24, 2, 21, 4, 12, 18, 10, 4, 24, 2, 36, 5, 12, 2, 20, 16, 6
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Divisors which are associates are identified (two Gaussian integers z1, z2 are associates if z1 = u * z2 where u is a unit, i.e. one of 1, i, -1, -i).
a(A004614(n)) = A000005(n). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 23 2003
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
Index entries for Gaussian integers and primes
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FORMULA
| Presumably a(n) = 2 iff n is a rational prime == 3 mod 4 (see A002145). - N. J. A. Sloane (njas(AT)research.att.com), Jan 07, 2003, Feb 23 2007
Multiplicative with a(2^e) = 2*e+1, a(p^e) = e+1 if p mod 4=3 and a(p^e) = (e+1)^2 if p mod 4=1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 23 2003
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EXAMPLE
| For example, 5 has divisors 1, 1+2i, 2+i and 5.
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MATHEMATICA
| Table[Length[Divisors[n, GaussianIntegers -> True]], {n, 30}] (* From Alonso del Arte, Jan 25 2011 *)
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PROG
| (Haskell)
a062327 n = product $ zipWith f (a027748_row n) (a124010_row n) where
f 2 e = 2 * e + 1
f p e | p `mod` 4 == 1 = (e + 1) ^ 2
| otherwise = e + 1
-- Reinhard Zumkeller, Oct 18 2011
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CROSSREFS
| Cf. A027748, A124010.
Sequence in context: A061313 A087669 A053087 * A075491 A089279 A049820
Adjacent sequences: A062324 A062325 A062326 * A062328 A062329 A062330
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KEYWORD
| nonn,nice,mult
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AUTHOR
| Reiner Martin (reinermartin(AT)hotmail.com), Jul 12 2001
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