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A297358 Numbers m such that the denominator of m/rho(m) is 3, where rho is A206369; i.e. A294649(m) = 3.

%I A297358 #13 Feb 11 2020 00:50:08
%S A297358 4,14,20,84,280,672,3360,4200,4214,6160,25284,36960,46200,57792,76160,
%T A297358 84280,92400,202272,288960,308700,656640,1011360,1142400,1264200,
%U A297358 1854160,2469600,3178560,11124960,12566400,13906200,22924160,27812400,107557632,120165120,212385600
%N A297358 Numbers m such that the denominator of m/rho(m) is 3, where rho is A206369; i.e. A294649(m) = 3.
%C A297358 The least instances for 4/3, 5/3, 7/3, 8/3, 10/3 and 11/3 are: 4, 20, 14, 672, 3360, 36960.
%C A297358 Then candidates for 13/3 and 14/3 are 54269201896764616671660406473798293913600000 and 23101697828019582727957348094429256309828763084415991060514234912131560924774400000000.
%e A297358 4 is a term because 4/A206369(4) = 4/3.
%e A297358 14 is a term because 14/A206369(14) = 14/6 = 7/3.
%t A297358 Select[Range[10^5], Denominator[#/(# DivisorSum[#, LiouvilleLambda[#]/# &])] == 3 &] (* _Michael De Vlieger_, Dec 29 2017 *)
%o A297358 (PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
%o A297358 rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
%o A297358 isok(n) = denominator(n/rho(n))==3;
%Y A297358 Cf. A206369 (rho), A294649, A295236 (analog with 2 instead of 3).
%Y A297358 Cf. A245775 (analog for sigma).
%K A297358 nonn
%O A297358 1,1
%A A297358 _Michel Marcus_, Dec 29 2017
%E A297358 a(33)-a(35) from _Jinyuan Wang_, Feb 10 2020