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Sum of totient function of primes dividing n is a prime.
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%I #11 Oct 27 2017 20:58:44

%S 3,6,9,10,12,14,18,20,22,24,26,27,28,30,34,36,38,40,44,46,48,50,52,54,

%T 56,58,60,62,66,68,70,72,74,76,80,81,82,86,88,90,92,94,96,98,100,102,

%U 104,106,108,112,116,118,120,122,124,130,132,134,136,140,142,144,146

%N Sum of totient function of primes dividing n is a prime.

%C Observe that this sequence includes even numbers and for all primes p as (a phi-sum) an infinite number of solutions exist, like e.g. (2^w)*p, with 1+p-1=p Phi-sum over its factors.

%H Michael De Vlieger, <a href="/A055632/b055632.txt">Table of n, a(n) for n = 1..10000</a>

%e If n=2^a*3^b*5^c*7^d*11^e then prime-factor set is {2,3,5,7,11}. The totient function values of this set are {1,2,4,6,10} and the sum is 1+2+4+6+10=23.

%t Select[Range@ 150, PrimeQ@ Total@ Map[EulerPhi@ # &, FactorInteger[#][[All, 1]]] &] (* _Michael De Vlieger_, Oct 26 2017 *)

%o (PARI) isok(n) = my(vp = factor(n)[,1]); isprime(sum(i=1, #vp, eulerphi(vp[i]))); \\ _Michel Marcus_, Dec 19 2013

%Y Cf. A001221, A006093, A053571, A055631.

%K nonn

%O 1,1

%A _Labos Elemer_, Jun 06 2000