A297358 - OEIS

%I #13 Feb 11 2020 00:50:08

%S 4,14,20,84,280,672,3360,4200,4214,6160,25284,36960,46200,57792,76160,

%T 84280,92400,202272,288960,308700,656640,1011360,1142400,1264200,

%U 1854160,2469600,3178560,11124960,12566400,13906200,22924160,27812400,107557632,120165120,212385600

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

%C 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 Then candidates for 13/3 and 14/3 are 54269201896764616671660406473798293913600000 and 23101697828019582727957348094429256309828763084415991060514234912131560924774400000000.

%e 4 is a term because 4/A206369(4) = 4/3.

%e 14 is a term because 14/A206369(14) = 14/6 = 7/3.

%t Select[Range[10^5], Denominator[#/(# DivisorSum[#, LiouvilleLambda[#]/# &])] == 3 &] (* _Michael De Vlieger_, Dec 29 2017 *)

%o (PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;

%o rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));

%o isok(n) = denominator(n/rho(n))==3;

%Y Cf. A206369 (rho), A294649, A295236 (analog with 2 instead of 3).

%Y Cf. A245775 (analog for sigma).

%K nonn

%O 1,1

%A _Michel Marcus_, Dec 29 2017

%E a(33)-a(35) from _Jinyuan Wang_, Feb 10 2020