A302252 Smallest number with exactly n divisors in Gaussian integers.

1, 3, 2, 5, 4, 6, 8, 15, 16, 12, 32, 10, 64, 24, 36, 65, 256, 48, 512, 20, 72, 96, 2048, 30, 324, 192, 50, 40, 16384, 252, 32768, 195, 288, 768, 648, 80, 262144, 1536, 576, 60, 1048576, 504, 2097152, 160, 100, 6144, 8388608, 130, 5832, 1875, 2304, 320

Offset

1,2

Comments

The divisors are counted up to association.

Links

Table of n, a(n) for n=1..52.

Index entries for Gaussian integers and primes

Formula

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

Mathematica

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 *)

Prog

(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
a(n) = {my(k=1); while (nbd(k) != n, k++); k; } \\ Michel Marcus, Apr 26 2018

Crossrefs

Cf. A005179, A062327.

Sequence in context: A054068 A194870 A355014 * A176988 A194903 A194875

Adjacent sequences: A302249 A302250 A302251 * A302253 A302254 A302255

Keyword

nonn

Author

Jianing Song, Apr 04 2018

Extensions

More terms from Giovanni Resta, Apr 04 2018

Status

approved