|
Search: id:A007663
|
|
|
| A007663 |
|
Fermat quotients: (2^(p-1)-1)/p, where p=prime(n).
(Formerly M2828)
|
|
+0
7
|
|
| 1, 3, 9, 93, 315, 3855, 13797, 182361, 9256395, 34636833, 1857283155, 26817356775, 102280151421, 1497207322929, 84973577874915, 4885260612740877, 18900352534538475, 1101298153654301589, 16628050996019877513
(list; graph; listen)
|
|
|
OFFSET
|
2,2
|
|
|
COMMENT
|
The only terms that are perfect squares are a(2) = 1 and a(4) = 9. - Nick Hobson (nickh(AT)qbyte.org), May 20 2007
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 105.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, 70.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=2..100
H. S. Vandiver, Fermat's Quotients And Related Arithmetic Functions
H. S. Vandiver, New Types Of Congruences Involving Bernoulli Numbers and Fermat's Quotient
H. S. Vandiver, On Congruences Which Relate The Fermat And Wilson Quotients To The Bernoulli Numbers
Nick Hobson, Fermat squares.
|
|
FORMULA
|
a(n) = 3*A096060(n) for n>2. a(n) = 3*A001045(prime(n)-1)/prime(n) for n>1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 01 2006
|
|
CROSSREFS
|
Cf. A002322, A001917, A096060, A001045.
Sequence in context: A067210 A018654 A003225 this_sequence A018695 A156336 A078221
Adjacent sequences: A007660 A007661 A007662 this_sequence A007664 A007665 A007666
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
