A066147 Numbers k such that all 3 of EulerPhi(k) + 1, d(k) + 1, sigma(k) + 1 are simultaneously prime (d(k) denotes the number of divisors of k).

1, 3, 5, 6, 10, 11, 12, 17, 22, 26, 27, 29, 38, 41, 46, 55, 59, 62, 71, 77, 82, 91, 99, 101, 106, 107, 108, 118, 125, 126, 132, 137, 145, 146, 149, 150, 158, 178, 179, 191, 197, 202, 206, 209, 216, 217, 218, 227, 234, 239, 262, 269, 276, 278, 281, 287, 302, 305

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Example

EulerPhi(12) + 1 = 5, d(12) + 1 = 7, sigma(12) + 1 = 29, all prime.

Mathematica

Select[Range[400], AllTrue[{EulerPhi[#]+1, DivisorSigma[0, #]+1, DivisorSigma[ 1, #]+1}, PrimeQ] &] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 16 2019 *)

Prog

(PARI) isok(m) = isprime(eulerphi(m) + 1) && isprime(numdiv(m) + 1) && isprime(sigma(m) + 1); \\ Harry J. Smith, Feb 02 2010

Crossrefs

Cf. A000005, A000010, A000203.

Sequence in context: A182637 A331915 A065512 * A175304 A140951 A190243

Adjacent sequences: A066144 A066145 A066146 * A066148 A066149 A066150

Keyword

nonn

Author

Joseph L. Pe, Dec 12 2001

Extensions

a(24)-a(58) from Harry J. Smith, Feb 02 2010

Status

approved