A302252 - OEIS

%I #23 Jul 29 2024 06:15:39

%S 1,3,2,5,4,6,8,15,16,12,32,10,64,24,36,65,256,48,512,20,72,96,2048,30,

%T 324,192,50,40,16384,252,32768,195,288,768,648,80,262144,1536,576,60,

%U 1048576,504,2097152,160,100,6144,8388608,130,5832,1875,2304,320

%N Smallest number with exactly n divisors in Gaussian integers.

%C The divisors are counted up to association.

%H Amiram Eldar, <a href="/A302252/b302252.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ga#gaussians">Index entries for Gaussian integers and primes</a>.

%F For prime p > 2, a(p) = 2^((p-1)/2) = sqrt(A005179(p)).

%t a[n_] := If[n > 2 && PrimeQ[n], 2^((n-1)/2), Block[{k=1}, While[ DivisorSigma[0, k, GaussianIntegers -> True] != n, k++]; k]]; Array[a, 52] (* _Giovanni Resta_, Apr 04 2018 *)

%o (PARI) nbd(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);}  \\ A062327

%o a(n) = {my(k=1); while (nbd(k) != n, k++); k;} \\ _Michel Marcus_, Apr 26 2018

%Y Cf. A005179, A062327.

%K nonn

%O 1,2

%A _Jianing Song_, Apr 04 2018

%E More terms from _Giovanni Resta_, Apr 04 2018