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.

A336488 Values taken by all the Jordan totient functions J_k(m) for k >= 1 and m >= 1.

This page as a plain text file.
%I A336488 #5 Jul 23 2020 03:27:35
%S A336488 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 A336488 48,52,54,56,58,60,63,64,66,70,72,78,80,82,84,88,92,96,100,102,104,
%U A336488 106,108,110,112,116,120,124,126,127,128,130,132,136,138,140,144,148
%N A336488 Values taken by all the Jordan totient functions J_k(m) for k >= 1 and m >= 1.
%C A336488 The asymptotic density of this sequence is 0 (Rao and Murty, 1979).
%C A336488 First differs from A221178 at n = 75, since a(75) = J_3(6) = 182 is not a term of A221178.
%H A336488 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 A336488 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 A336488 A002202 is a subsequence.
%Y A336488 Cf. A000010, A007434, A059376, A059377, A059378, A059379, A059380, A069091, A069092, A069093, A069094, A069095, A221178.
%Y A336488 Similar sequence: A211347.
%K A336488 nonn
%O A336488 1,2
%A A336488 _Amiram Eldar_, Jul 23 2020