A296580 Odd primes p such that tau(p) is congruent to (p-1)/2 (mod p), where tau is the Ramanujan tau function (A000594).

191, 5399, 1259393

Offset: 1

Author

Seiichi Manyama, Dec 16 2017

Keywords

• nonn
• more

Comments

a(4) > 10^7.

There is no odd prime p (< 10^7) such that tau(p) is congruent to (p+1)/2 (mod p).

Examples

			tau(191) = 2762403350592 and 2762403350592 == 95 mod 191, so a(1) = 191.
tau(5399) = -616400667743946780600 and -616400667743946780600 == 2699 mod 5399, so a(2) = 5399.
tau(1259393) = -600367974333827988240021654527358 and -600367974333827988240021654527358 == 629696 mod 1259393, so a(3) = 1259393.
		

Links

• Eric Weisstein's World of Mathematics, Tau Function.
• Wikipedia, Ramanujan tau function

Crossrefs

Cf. A000594, A007659, A076847 (tau(p)), A193855, A273650, A273651, A295645.