A066814 Smallest prime p such that (p-1) has n divisors, or 0 if no such prime exists.

2, 3, 5, 7, 17, 13, 0, 31, 37, 113, 0, 61, 0, 193, 401, 211, 65537, 181, 0, 241, 577, 13313, 0, 421, 1297, 12289, 4357, 2113, 0, 1009, 0, 1321, 25601, 2424833, 752734097, 1801, 0, 786433, 495617, 2161, 0, 4801, 0, 15361, 7057, 155189249, 0

Offset: 1

Author

Wouter Meeussen, Jan 20 2002

Keywords

• nonn

Comments

The only primes p for which p-1 has a prime number of divisors are Fermat primes A019434.

Examples

			a(17)=65537 because DivisorSigma[0,65536]=17.
		

Crossrefs

Cf. A004249, A007516, A066529.

Programs

Mathematica

it=Table[ p=Prime[ n ]; DivisorSigma[ 0, p-1 ], {n, 400000} ]; Flatten[ Position[ it, #, 1, 1 ]&/@Range[ 100 ]/.{}- > 0 ]

Extensions

Comment clarified by T. D. Noe, Nov 06 2009

Edited by Max Alekseyev, Nov 10 2009