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Search: id:A103225
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| A103225 |
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Number of Gaussian integers z with abs(z) < n and gcd(n,z)=1. |
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+0
1
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| 1, 4, 24, 24, 44, 48, 144, 96, 224, 96, 372, 192, 444, 304, 404, 392, 792, 448, 1124, 408, 1200, 752, 1648, 808, 1240, 896, 2036, 1200, 2440, 800, 2996, 1600, 3008, 1592, 2404, 1808, 4056, 2256, 3616, 1600, 4992, 2400, 5784, 3008, 3604, 3304, 6916, 3224, 7376
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This sequence is much like the usual totient function. That is, it gives the number of Gaussian integers that are relatively prime to n and whose modulus is less than n. When n is a Gaussian prime, A002145, then a(n) = A051132(n)-1.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..200
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EXAMPLE
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a(2)=4 because 1, -1, i and -i are relatively prime to 2 and have modulus less than 2.
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MATHEMATICA
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Table[cnt=0; Do[z=a+ b*I; If[Abs[z]<n && GCD[n, z]==1, cnt++ ], {a, -n+1, n-1}, {b, -n+1, n-1}]; cnt, {n, 60}]
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CROSSREFS
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Sequence in context: A145514 A024543 A010294 this_sequence A137980 A144137 A166727
Adjacent sequences: A103222 A103223 A103224 this_sequence A103226 A103227 A103228
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KEYWORD
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nice,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 26 2005
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