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Primes p such that Ramanujan number tau(p) is divisible by p.
(Formerly M0681)
11

%I M0681 #30 Jun 06 2022 16:11:01

%S 2,3,5,7,2411,7758337633

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

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

%D J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 275.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H F. Q. Gouvea (1997) <a href="http://www.emis.de/journals/EM/restricted/6/6.3/gouvea.ps">Non-ordinary primes: a story</a>, Experimental Mathematics 6(3), 195-205.

%H N. Lygeros and O. Rozier (2010) <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL13/Lygeros/lygeros5.pdf">A new solution for the equation tau(p)=0 (mod p)</a>. Journal of Integer Sequences 13, Article 10.7.4.

%H N. Lygeros. <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;ebbe2767.1003">A new solution for the equation tau(p)=0 mod p</a>. Number Theory mailing list (NMBRTHRY).

%t (* First do *) <<NumberTheory`Ramanujan` (* then *) Select[ Prime[ Range[ 5133]], Mod[ RamanujanTau[ # ], # ] == 0 &] (* _Dean Hickerson_, Jan 03 2003 *)

%t Select[Prime[Range[400]],Divisible[RamanujanTau[#],#]&] (* The program generates the first 5 terms of the sequence. *) (* _Harvey P. Dale_, Jun 06 2022 *)

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

%K hard,nonn,more

%O 1,1

%A _N. J. A. Sloane_, _Robert G. Wilson v_

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

%E Edited by _Max Alekseyev_, Jul 11 2010