A055632 Sum of totient function of primes dividing n is a prime.

3, 6, 9, 10, 12, 14, 18, 20, 22, 24, 26, 27, 28, 30, 34, 36, 38, 40, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 80, 81, 82, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 112, 116, 118, 120, 122, 124, 130, 132, 134, 136, 140, 142, 144, 146

Offset: 1

Author

Labos Elemer, Jun 06 2000

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A006093, A053571, A055631.

Programs

Mathematica

Select[Range@ 150, PrimeQ@ Total@ Map[EulerPhi@ # &, FactorInteger[#][[All, 1]]] &] (* Michael De Vlieger, Oct 26 2017 *)

PARI

isok(n) = my(vp = factor(n)[,1]); isprime(sum(i=1, #vp, eulerphi(vp[i]))); \\ Michel Marcus, Dec 19 2013