cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A053198 Totients of consecutive pure powers of primes.

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%I A053198 #14 Dec 21 2020 02:26:23
%S A053198 2,4,6,8,20,18,16,42,32,54,110,100,64,156,162,128,272,294,342,256,506,
%T A053198 500,486,812,930,512,1210,1332,1640,1806,1024,1458,2028,2162,2058,
%U A053198 2756,2500,3422,3660,2048,4422,4624,4970,5256,6162,4374,6498,6806,7832,4096
%N A053198 Totients of consecutive pure powers of primes.
%C A053198 Totients of prime powers are prime powers only for powers of 2.
%H A053198 Amiram Eldar, <a href="/A053198/b053198.txt">Table of n, a(n) for n = 1..10000</a>
%F A053198 a(n) = A000010(A025475(n+1)).
%F A053198 Numbers of the form phi(p^k) = (p-1)*p^(k-1), where p is prime and k > 1.
%F A053198 Sum_{n>=1} 1/a(n) = Sum_{p prime} 1/(p-1)^2 = A086242 = 1.3750649947... - _Amiram Eldar_, Dec 21 2020
%e A053198 The 10th pure power of prime (but not a prime) is 81, so a(10) = EulerPhi(81) = 54.
%t A053198 EulerPhi[Select[Range[2^13], CompositeQ[#] && PrimePowerQ[#] &]] (* _Amiram Eldar_, Dec 21 2020 *)
%Y A053198 Cf. A000010, A051953, A001248, A002618, A036689, A053650, A053191, A053192, A086242.
%K A053198 nonn
%O A053198 1,1
%A A053198 _Labos Elemer_, Mar 03 2000