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 A062327 Number of divisors of n over the Gaussian integers. 18
 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; text; internal format)
 OFFSET 1,2 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, Jan 23 2003 a(A004613(n)) = A000005(n)^2. - Benedikt Otten, May 22 2013 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 FORMULA Presumably a(n) = 2 iff n is a rational prime == 3 mod 4 (see A045326). - N. J. A. Sloane, 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, Jan 23 2003 EXAMPLE For example, 5 has divisors 1, 1+2i, 2+i and 5. MATHEMATICA Table[Length[Divisors[n, GaussianIntegers -> True]], {n, 30}] (* Alonso del Arte, Jan 25 2011 *) DivisorSigma[0, Range, GaussianIntegers->True] (* Harvey P. Dale, Mar 19 2017 *) 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 (PARI) a(n)= {     my(r=1, f=factor(n));     for(j=1, #f[, 1], my(p=f[j, 1], e=f[j, 2]);         if(p==2, r*=(2*e+1));         if(p%4==1, r*=(e+1)^2);         if(p%4==3, r*=(e+1));     );     return(r); }  \\ Joerg Arndt, Dec 09 2016 CROSSREFS Cf. A027748, A124010. Sequence in context: A087669 A053087 A316519 * A075491 A326730 A089279 Adjacent sequences:  A062324 A062325 A062326 * A062328 A062329 A062330 KEYWORD nonn,nice,mult AUTHOR Reiner Martin (reinermartin(AT)hotmail.com), Jul 12 2001 STATUS approved

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Last modified May 8 08:09 EDT 2021. Contains 343658 sequences. (Running on oeis4.)