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A302252 Smallest number with exactly n divisors in Gaussian integers. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A194837 A054068 A194870 * 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

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Last modified July 30 06:21 EDT 2021. Contains 346348 sequences. (Running on oeis4.)