A007659 Primes p such that Ramanujan number tau(p) is divisible by p. (Formerly M0681)

2, 3, 5, 7, 2411, 7758337633

Offset

1,1

Comments

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

References

J. 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

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

F. Q. Gouvea (1997) Non-ordinary primes: a story, Experimental Mathematics 6(3), 195-205.

N. Lygeros and O. Rozier (2010) A new solution for the equation tau(p)=0 (mod p). Journal of Integer Sequences 13, Article 10.7.4.

N. Lygeros. A new solution for the equation tau(p)=0 mod p. Number Theory mailing list (NMBRTHRY).

Mathematica

(* First do *) <<NumberTheory`Ramanujan` (* then *) 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 *)

Crossrefs

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

Sequence in context: A212667 A252357 A037948 * A288715 A208361 A145380

Adjacent sequences: A007656 A007657 A007658 * A007660 A007661 A007662

Keyword

hard,nonn,more

Author

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

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

Status

approved