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A066147 Numbers n such that all 3 of EulerPhi(n) + 1, d(n) + 1, sigma(n) + 1 are simultaneously prime (d(n) denotes the number of divisors of n). 1
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 (list; graph; refs; listen; history; text; internal format)
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) { n=0; for (m=1, 10^9, if (isprime(eulerphi(m) + 1) && isprime(numdiv(m) + 1) && isprime(sigma(m) + 1), write("b066147.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Feb 02 2010

CROSSREFS

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

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Last modified November 28 13:47 EST 2021. Contains 349413 sequences. (Running on oeis4.)