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.
%I A380500 #30 Feb 19 2025 16:17:35
%S A380500 1,1,1,1,1,1,1,2,2,2,1,2,8,6,4,1,4,12,40,18,8,1,4,40,84,200,54,16,1,8,
%T A380500 48,440,588,1000,162,32,1,6,128,624,4840,4116,5000,486,64,1,10,108,
%U A380500 2176,8112,53240,28812,25000,1458,128,1,12,220,2052,36992,105456,585640,201684,125000,4374,256
%N A380500 Table T(n,k) = phi(phi(prime(n)^k)), n >= 1, k >= 0, read by upwards antidiagonals, where phi = A000010.
%C A380500 For n >= 2, k >= 1, T(n,k) is the number of primitive roots of prime(n)^k.
%H A380500 Michael De Vlieger, <a href="/A380500/b380500.txt">Table of n, a(n) for n = 1..11476</a> (rows n = 1..150, flattened).
%F A380500 T(n,k) = A010554(prime(n)^k) = A046144(prime(n)^k).
%F A380500 T(n,0) = 1.
%F A380500 T(n,1) = phi(prime(n)-1) = A008330(n).
%F A380500 T(n,2) = (prime(n)-1) * phi(prime(n)-1)
%F A380500 = (prime(n)-1)^2 * Product_{q|(prime(n)-1)} 1-1/q, prime q.
%F A380500 = A104039(n).
%F A380500 For k > 1, T(n,k) = prime(n)^(k-2) * A104039(n).
%F A380500 T(n,2) > prime(n) for n > 2.
%F A380500 T(n,k) < prime(n)^k for all n and for k > 0.
%e A380500 Table begins as follows:
%e A380500 n\k 0 1 2 3 4 5 6 7
%e A380500 ---------------------------------------------------------------
%e A380500 1: 1 1 1 2 4 8 16 32
%e A380500 2: 1 1 2 6 18 54 162 486
%e A380500 3: 1 2 8 40 200 1000 5000 25000
%e A380500 4: 1 2 12 84 588 4116 28812 201684
%e A380500 5: 1 4 40 440 4840 53240 585640 6442040
%e A380500 6: 1 4 48 624 8112 105456 1370928 17822064
%e A380500 7: 1 8 128 2176 36992 628864 10690688 181741696
%t A380500 Table[EulerPhi[EulerPhi[Prime[#]^k]] &[n - k + 1], {n, 0, 10}, {k, 0, n}] // Flatten
%Y A380500 Cf. A000010, A000040, A001248, A008330, A010554, A046144, A104039, A246655.
%K A380500 nonn,easy,tabl
%O A380500 1,8
%A A380500 _Michael De Vlieger_, Feb 04 2025