A007659 Primes p such that Ramanujan number tau(p) is divisible by p.

2, 3, 5, 7, 2411, 7758337633

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• hard
• nonn
• more

Comments

Primes at which cusp form Delta_12 (see A007332) is not ordinary.

a(5) was found by Newman (1972). - Amiram Eldar, Jan 06 2025

References

• Morris Newman, A table of tau(p) modulo p, p prime, 3 <= p <= 16067, National Bureau of Standards, 1972.
• Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 275.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Fernando Q. Gouvêa, Non-ordinary primes: a story, Experimental Mathematics 6(3) (1997), 195-205; alternative link.
• Nik Lygeros and Olivier Rozier, A new solution for the equation tau(p)=0 (mod p). Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.4.
• Nik Lygeros and Olivier Rozier, A new solution for the equation tau(p)=0 mod p. Number Theory mailing list (NMBRTHRY), 2010.
• Morris Newman, A table of tau(p) modulo p, p prime, 3 <= p <= 16067, Review, Mathematics of Computation, Vol. 27, No. 121 (1973), pp. 215-216.

Crossrefs

Cf. A000594, A007332. A proper subset of A063938.

Programs

Mathematica

Select[ Prime[ Range[ 5133]], Mod[ RamanujanTau[ # ], # ] == 0 &] (* Dean Hickerson, Jan 03 2003 *)
Select[Prime[Range[400]],Divisible[RamanujanTau[#],#]&] (* The program generates the first 5 terms of the sequence. *) (* Harvey P. Dale, Jun 06 2022 *)

Extensions

a(6) = 7758337633 from N. Lygeros and O. Rozier, Mar 16 2010. - N. J. A. Sloane, Mar 16 2010

Edited by Max Alekseyev, Jul 11 2010