

A085623


Let p = nth 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
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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

T. D. Noe, Table of n, a(n) for n = 2..1000
Yaming Lu and Yuan Yi, On the generalization of the D. H. Lehmer problem II, Acta Arithm. vol 142 no 2 (2010), 179186.
Yuan Yi and Zhang Wenpeng, On the generalization of a problem of D. H. Lehmer, Kyushu J. Math., 56 (2002) 235241; 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 A190791 A002885
Adjacent sequences: A085620 A085621 A085622 * A085624 A085625 A085626


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



