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%I #12 Sep 16 2019 15:21:18
%S 1,3,5,6,10,11,12,17,22,26,27,29,38,41,46,55,59,62,71,77,82,91,99,101,
%T 106,107,108,118,125,126,132,137,145,146,149,150,158,178,179,191,197,
%U 202,206,209,216,217,218,227,234,239,262,269,276,278,281,287,302,305
%N 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).
%H Harry J. Smith, <a href="/A066147/b066147.txt">Table of n, a(n) for n = 1..1000</a>
%e EulerPhi(12) + 1 = 5, d(12) + 1 = 7, sigma(12) + 1 = 29, all prime.
%t 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 *)
%o (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
%K nonn
%O 1,2
%A _Joseph L. Pe_, Dec 12 2001
%E a(24)-a(58) from _Harry J. Smith_, Feb 02 2010