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A072273 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. 1
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; text; internal format)
OFFSET

1,8

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

FORMULA

2^a(n) = A060594(n).

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).

MATHEMATICA

Log[2, Table[cnt=0; Do[If[Mod[k^2-1, n]==0, cnt++ ], {k, n}]; cnt, {n, 150}]] (*_ T. D. Noe_ *)

PROG

(PARI)

A072273(n) = if(n<=2, 0, #znstar(n)[3] ); \\ After Joerg Arndt's code for A060594

A072273(n) = {my(o=valuation(n, 2)); (omega(n>>o)+max(min(o-1, 2), 0)); }; \\ Or after Charles R Greathouse IV code for A060594.

\\ Antti Karttunen, Aug 22 2017

CROSSREFS

Cf. A060594.

Cf. A046072. [From R. J. Mathar, Dec 15 2008]

Sequence in context: A215975 A071891 A046072 * A157230 A034380 A077479

Adjacent sequences:  A072270 A072271 A072272 * A072274 A072275 A072276

KEYWORD

nonn

AUTHOR

Lekraj Beedassy, Jul 09 2002

EXTENSIONS

Corrected and extended by T. D. Noe, Sep 09 2005

STATUS

approved

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Last modified December 12 03:27 EST 2018. Contains 318052 sequences. (Running on oeis4.)