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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

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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