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%I #5 Jul 23 2020 03:27:35
%S 1,2,3,4,6,7,8,10,12,15,16,18,20,22,24,26,28,30,31,32,36,40,42,44,46,
%T 48,52,54,56,58,60,63,64,66,70,72,78,80,82,84,88,92,96,100,102,104,
%U 106,108,110,112,116,120,124,126,127,128,130,132,136,138,140,144,148
%N Values taken by all the Jordan totient functions J_k(m) for k >= 1 and m >= 1.
%C The asymptotic density of this sequence is 0 (Rao and Murty, 1979).
%C First differs from A221178 at n = 75, since a(75) = J_3(6) = 182 is not a term of A221178.
%H R. Sita Rama Chandra Rao and G. Sri Rama Chandra Murty, <a href="https://doi.org/10.4153/CMB-1979-018-5">On a theorem of Niven</a>, Canadian Mathematical Bulletin, Vol 22, No. 1 (1979), pp. 113-115.
%t phiQ[m_] := Select[Range[m + 1, 2 m*Product[(1 - 1/(k*Log[k]))^(-1), {k, 2, DivisorSigma[0, m]}]], EulerPhi[#] == m &, 1] != {}; jor[k_, n_] := DivisorSum[n, #^k*MoebiusMu[n/#] &]; jorval[k_, mx_] := jor[k, #] & /@ Range[Floor@Surd[mx*Zeta[k], k]]; mx = 300; Select[Union @ Flatten[{Select[Range[mx], phiQ], jorval[#, mx] & /@ Range[2, Floor[Log2[mx]]]}], # <= mx &] (* using code by _Jean-François Alcover_ at A002202 *)
%Y A002202 is a subsequence.
%Y Cf. A000010, A007434, A059376, A059377, A059378, A059379, A059380, A069091, A069092, A069093, A069094, A069095, A221178.
%Y Similar sequence: A211347.
%K nonn
%O 1,2
%A _Amiram Eldar_, Jul 23 2020
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