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A302252
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Smallest number with exactly n divisors in Gaussian integers.
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1
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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
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OFFSET
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1,2
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COMMENTS
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The divisors are counted up to association.
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LINKS
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FORMULA
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For prime p > 2, a(p) = 2^((p-1)/2) = sqrt(A005179(p)).
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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