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A262339 Exceptional primes for Ramanujan's tau function. 2
2, 3, 5, 7, 23, 691 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For each exceptional prime p, Ramanujan's tau function tau(n) = A000594(n) satisfies a simple congruence modulo p.

The main entry for this subject is A000594.

REFERENCES

H. P. F. Swinnerton-Dyer, Congruence properties of tau(n), pp. 289-311 of G. E. Andrews et al., editors, Ramanujan Revisited. Academic Press, NY, 1988.

LINKS

Table of n, a(n) for n=1..6.

H. P. F. Swinnerton-Dyer, On l-adic representations and congruences for coefficients of modular forms, pp. 1-55 of Modular Functions of One Variable III (Antwerp 1972), Lect. Notes Math., 350, 1973.

Wikipedia, Ramanujan tau function

EXAMPLE

691 is an exceptional prime because tau(n) == sum of 11th power of divisors of n mod 691 (see A046694).

CROSSREFS

Cf. A000594, A046694.

Sequence in context: A289754 A062088 A070029 * A110094 A088054 A249509

Adjacent sequences:  A262336 A262337 A262338 * A262340 A262341 A262342

KEYWORD

nonn,fini,full

AUTHOR

Jonathan Sondow, Sep 18 2015

STATUS

approved

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Last modified February 22 18:05 EST 2019. Contains 320400 sequences. (Running on oeis4.)