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A007659
Primes p such that Ramanujan number tau(p) is divisible by p.
(Formerly M0681)
11
2, 3, 5, 7, 2411, 7758337633
OFFSET
1,1
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. GouvĂȘa, 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.
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 *)
CROSSREFS
Cf. A000594, A007332. A proper subset of A063938.
Sequence in context: A212667 A252357 A037948 * A375936 A288715 A208361
KEYWORD
hard,nonn,more
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