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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
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, 48, 64, 62, 66, 40, 68, 66, 72, 90, 68, 70, 84, 92, 90, 100, 90, 80, 98, 102, 88, 88, 108, 108, 106, 126, 116, 126, 112, 134, 136, 150, 116, 142, 146, 144, 146, 136, 156, 158, 178
OFFSET
2,2
COMMENTS
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]
REFERENCES
R. K. Guy, Unsolved Problems in Number Theory, F12.
LINKS
Yaming Lu and Yuan Yi, On the generalization of the D. H. Lehmer problem II, Acta Arithm. vol 142 no 2 (2010), 179-186.
Yuan Yi and Zhang Wen-peng, On the generalization of a problem of D. H. Lehmer, Kyushu J. Math., 56 (2002) 235-241; MR 2003g:11112.
EXAMPLE
For p = 13, the pairs are (2,7), (5,8), (6,11) and their reversals. So a(6) = 6.
MATHEMATICA
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}]
CROSSREFS
Cf. A201652.
Sequence in context: A066659 A343468 A287846 * A317965 A369025 A190791
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, based on a suggestion of R. K. Guy, Jul 11 2003
EXTENSIONS
Extended by Vladeta Jovovic and Robert G. Wilson v, Jul 12 2003
Removed the "odd" attribute from the primes in the definition (see the offset) - R. J. Mathar, Aug 07 2010
STATUS
approved