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A132213
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Number of distinct primes among the squares mod n.
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3
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0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 1, 3, 0, 0, 2, 2, 4, 1, 1, 3, 3, 0, 2, 4, 3, 0, 4, 1, 4, 1, 2, 4, 2, 1, 3, 6, 2, 0, 5, 2, 6, 2, 2, 7, 5, 0, 6, 5, 3, 3, 8, 6, 3, 0, 3, 6, 8, 0, 6, 8, 3, 2, 2, 3, 7, 3, 3, 2, 7, 0, 9, 10, 3, 4, 6, 4, 9, 1, 10, 10, 11, 1, 2, 13, 3, 0, 10, 4, 5, 4, 4, 13, 4, 1, 11, 10, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,11
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COMMENTS
| It appears that a(n)=0 for only the 30 numbers in A065428, which appears to be related to idoneal numbers, A000926. The graph shows a(n) can be quite small even for large n. For example, a(9240)=7. Observe that the graph up to n=10000 appears to have 5 components. Why?
The logarithmic plot of the first 10^6 terms shows seven components.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
T. D. Noe, Logarithmic plot of 10^6 terms
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EXAMPLE
| For n=14, the squares (mod n) repeat 0,1,4,9,2,11,8,7,8,11,2,9,4,1,0,..., a sequence containing three distinct primes: 2, 7 and 11. Hence a(14)=3.
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MATHEMATICA
| Table[s=Union[Mod[Range[n]^2, n]]; Length[Select[s, PrimeQ]], {n, 10000}]
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PROG
| (Haskell)
import Data.List (nub)
a132213 n = sum $
map a010051 $ nub $ take n $ map (`mod` n) $ tail a000290_list
-- Reinhard Zumkeller, Oct 15 2011
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CROSSREFS
| Cf. A000224 (number of squares mod n).
Cf. A000290, A010051.
Sequence in context: A004199 A062283 A136493 * A202502 A154312 A119900
Adjacent sequences: A132210 A132211 A132212 * A132214 A132215 A132216
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KEYWORD
| nice,nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Aug 13 2007, Aug 17 2007
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