A053198 Totients of consecutive pure powers of primes.

2, 4, 6, 8, 20, 18, 16, 42, 32, 54, 110, 100, 64, 156, 162, 128, 272, 294, 342, 256, 506, 500, 486, 812, 930, 512, 1210, 1332, 1640, 1806, 1024, 1458, 2028, 2162, 2058, 2756, 2500, 3422, 3660, 2048, 4422, 4624, 4970, 5256, 6162, 4374, 6498, 6806, 7832, 4096

Offset: 1

Author

Labos Elemer, Mar 03 2000

Keywords

• nonn

Comments

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

EulerPhi[Select[Range[2^13], CompositeQ[#] && PrimePowerQ[#] &]] (* Amiram Eldar, Dec 21 2020 *)

Formula

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

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

Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p-1)^2 = A086242 = 1.3750649947... - Amiram Eldar, Dec 21 2020