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 A085623 Let p = n-th prime; a(n) = number of pairs (i,j) with 0 < i < p, 0 < j < p such that ij == 1 mod p and i and j have opposite parity. 2

%I

%S 0,2,0,4,6,10,4,12,18,4,14,18,20,16,30,32,30,20,28,34,32,40,46,54,46,

%T 48,64,62,66,40,68,66,72,90,68,70,84,92,90,100,90,80,98,102,88,88,108,

%U 108,106,126,116,126,112,134,136,150,116,142,146,144,146,136,156,158,178

%N Let p = n-th prime; a(n) = number of pairs (i,j) with 0 < i < p, 0 < j < p such that ij == 1 mod p and i and j have opposite parity.

%C If we let p=2n+1 run through all odd numbers >=3 and consider only i coprime to p, the sequence becomes 0, 2, 0, 4, 4, 6, 0, 10, 4, 4, 12, 14, 8, 18, 4, 12, 12, 14, 8, 18... [R. J. Mathar, Aug 07 2010]

%D R. K. Guy, Unsolved Problems in Number Theory, F12.

%H T. D. Noe, <a href="/A085623/b085623.txt">Table of n, a(n) for n = 2..1000</a>

%H Yaming Lu and Yuan Yi, <a href="http://dx.doi.org/10.4064/aa142-2-7">On the generalization of the D. H. Lehmer problem II</a>, Acta Arithm. vol 142 no 2 (2010), 179-186.

%H Yuan Yi and Zhang Wen-peng, <a href="http://dx.doi.org/10.2206/kyushujm.56.235">On the generalization of a problem of D. H. Lehmer</a>, Kyushu J. Math., 56 (2002) 235-241; MR 2003g:11112.

%e For p = 13, the pairs are (2,7), (5,8), (6,11) and their reversals. So a(6) = 6.

%t f[n_] := Length[ Select[ Mod[ Flatten[ Table[i*j, {j, 2, n - 1}, {i, j - 1, 1, -2}], 1], n], # == 1 & ]]; 2Table[ f[ Prime[n]], {n, 2, 70}]

%Y Cf. A201652.

%K nonn,easy

%O 2,2

%A _N. J. A. Sloane_, based on a suggestion of _R. K. Guy_, Jul 11 2003

%E Extended by _Vladeta Jovovic_ and _Robert G. Wilson v_, Jul 12 2003

%E Removed the "odd" attribute from the primes in the definition (see the offset) - _R. J. Mathar_, Aug 07 2010

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Last modified August 3 13:59 EDT 2021. Contains 346438 sequences. (Running on oeis4.)