cp's OEIS Frontend

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

%I A007659 M0681 #39 Jan 07 2025 02:38:34
%S A007659 2,3,5,7,2411,7758337633
%N A007659 Primes p such that Ramanujan number tau(p) is divisible by p.
%C A007659 Primes at which cusp form Delta_12 (see A007332) is not ordinary.
%C A007659 a(5) was found by Newman (1972). - _Amiram Eldar_, Jan 06 2025
%D A007659 Morris Newman, A table of tau(p) modulo p, p prime, 3 <= p <= 16067, National Bureau of Standards, 1972.
%D A007659 Joe Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 275.
%D A007659 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007659 Fernando Q. Gouvêa, <a href="http://www.emis.de/journals/EM/restricted/6/6.3/gouvea.ps">Non-ordinary primes: a story</a>, Experimental Mathematics 6(3) (1997), 195-205; <a href="https://projecteuclid.org/journals/experimental-mathematics/volume-6/issue-3/Non-ordinary-primes-a-story/em/1047920420.full">alternative link</a>.
%H A007659 Nik Lygeros and Olivier Rozier, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Lygeros/lygeros5.html">A new solution for the equation tau(p)=0 (mod p)</a>. Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.4.
%H A007659 Nik Lygeros and Olivier Rozier, <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), 2010.
%H A007659 Morris Newman, <a href="https://doi.org/10.2307/2005272">A table of tau(p) modulo p, p prime, 3 <= p <= 16067</a>, Review, Mathematics of Computation, Vol. 27, No. 121 (1973), pp. 215-216.
%t A007659 Select[ Prime[ Range[ 5133]], Mod[ RamanujanTau[ # ], # ] == 0 &] (* _Dean Hickerson_, Jan 03 2003 *)
%t A007659 Select[Prime[Range[400]],Divisible[RamanujanTau[#],#]&] (* The program generates the first 5 terms of the sequence. *) (* _Harvey P. Dale_, Jun 06 2022 *)
%Y A007659 Cf. A000594, A007332. A proper subset of A063938.
%K A007659 hard,nonn,more
%O A007659 1,1
%A A007659 _N. J. A. Sloane_, _Robert G. Wilson v_
%E A007659 a(6) = 7758337633 from N. Lygeros and O. Rozier, Mar 16 2010. - _N. J. A. Sloane_, Mar 16 2010
%E A007659 Edited by _Max Alekseyev_, Jul 11 2010