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A053198
Totients of consecutive pure powers of primes.
2
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
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 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Mar 03 2000
STATUS
approved