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Search: id:A000224
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| A000224 |
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Number of squares mod n. |
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+0
25
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| 1, 2, 2, 2, 3, 4, 4, 3, 4, 6, 6, 4, 7, 8, 6, 4, 9, 8, 10, 6, 8, 12, 12, 6, 11, 14, 11, 8, 15, 12, 16, 7, 12, 18, 12, 8, 19, 20, 14, 9, 21, 16, 22, 12, 12, 24, 24, 8, 22, 22, 18, 14, 27, 22, 18, 12, 20, 30, 30, 12, 31, 32, 16, 12, 21
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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E. J. F. Primrose, The number of quadratic residues mod m, Math. Gaz. v. 61 (1977) n. 415, 60-61.
W. D. Stangl, Counting squares in Z_n, Math. Mag. 69 (1996) 285-289.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
S. R. Finch and Pascal Sebah, Squares and Cubes Modulo n (arXiv:math.NT/0604465).
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FORMULA
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Multiplicative with a(p^e) = [p^e/6]+2 if p = 2; [p^(e+1)/(2p+2)]+1 if p > 2. - David W. Wilson (davidwwilson(AT)comcast.net), Aug 01, 2001.
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MAPLE
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seq(nops({seq(n^2 mod k, n=1..100)}), k=1..65); (E. Deutsch)
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PROGRAM
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(PARI) a(n) = local(v, i); v = vector(n, i, 0); for(i=0, floor(n/2), v[i^2%n+1] = 1); sum(i=1, n, v[i]) - Franklin T. Adams-Watters, Nov 05 2006
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CROSSREFS
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a(n)=A105612(n)+1.
Sequence in context: A144000 A085202 A096009 this_sequence A085201 A051601 A054225
Adjacent sequences: A000221 A000222 A000223 this_sequence A000225 A000226 A000227
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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