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

1,1

Comments

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

Links

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

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A133296 A323333 A076402 * A249278 A273892 A352546

Adjacent sequences: A053195 A053196 A053197 * A053199 A053200 A053201

Keyword

nonn

Author

Labos Elemer, Mar 03 2000

Status

approved