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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 (list; graph; refs; listen; history; text; internal format)
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), 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 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

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Last modified June 18 07:25 EDT 2021. Contains 345098 sequences. (Running on oeis4.)