A262339 Exceptional primes for Ramanujan's tau function.

2, 3, 5, 7, 23, 691

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.

Terms 23 and 691 also appear in A193855. - Jud McCranie, Nov 05 2020

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, A193855.

Sequence in context: A070029 A360497 A368805 * A110094 A088054 A249509

Adjacent sequences: A262336 A262337 A262338 * A262340 A262341 A262342

Keyword

nonn,fini,full

Author

Jonathan Sondow, Sep 18 2015

Status

approved