A053198 - OEIS

%I #14 Dec 21 2020 02:26:23

%S 2,4,6,8,20,18,16,42,32,54,110,100,64,156,162,128,272,294,342,256,506,

%T 500,486,812,930,512,1210,1332,1640,1806,1024,1458,2028,2162,2058,

%U 2756,2500,3422,3660,2048,4422,4624,4970,5256,6162,4374,6498,6806,7832,4096

%N Totients of consecutive pure powers of primes.

%C Totients of prime powers are prime powers only for powers of 2.

%H Amiram Eldar, <a href="/A053198/b053198.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000010(A025475(n+1)).

%F Numbers of the form phi(p^k) = (p-1)*p^(k-1), where p is prime and k > 1.

%F Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p-1)^2 = A086242 = 1.3750649947... - _Amiram Eldar_, Dec 21 2020

%e The 10th pure power of prime (but not a prime) is 81, so a(10) = EulerPhi(81) = 54.

%t EulerPhi[Select[Range[2^13], CompositeQ[#] && PrimePowerQ[#] &]] (* _Amiram Eldar_, Dec 21 2020 *)

%Y Cf. A000010, A051953, A001248, A002618, A036689, A053650, A053191, A053192, A086242.

%K nonn

%O 1,1

%A _Labos Elemer_, Mar 03 2000