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A072273
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Index of powers of 2 that equal the number of noncongruent roots to the congruence x^2=k (mod n) for (k,n)=1 and assuming solvability.
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0
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0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 3, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 3, 1, 2, 1, 2, 2, 1, 1, 3, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 3, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 2, 2, 1, 3, 1, 1, 1, 3, 2, 1, 2, 3, 1, 2, 2, 2, 2, 1, 2, 3, 1, 1, 2, 2, 1, 2, 1, 3, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,8
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COMMENTS
| 2^a(n) = A060594
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FORMULA
| a(n) = A005087(n) + i, where i may be 0, 1 or 2 according as 2^j divides n, respectively with j <= 1, j=2 or j>=3, (i.e. i=0 when n is not divisible by 4; i=1 when n is divisible by 4 but not by 8; i=2 when n is divisible by 8).
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MATHEMATICA
| Log[2, Table[cnt=0; Do[If[Mod[k^2-1, n]==0, cnt++ ], {k, n}]; cnt, {n, 150}]] (Noe)
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CROSSREFS
| Cf. A060594.
Cf. A046072. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
Sequence in context: A103961 A071891 A046072 * A157230 A034380 A077479
Adjacent sequences: A072270 A072271 A072272 * A072274 A072275 A072276
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KEYWORD
| nonn
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 09 2002
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EXTENSIONS
| Corrected and extended by T. D. Noe (noe(AT)sspectra.com), Sep 09 2005
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