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

4, 14, 20, 84, 280, 672, 3360, 4200, 4214, 6160, 25284, 36960, 46200, 57792, 76160, 84280, 92400, 202272, 288960, 308700, 656640, 1011360, 1142400, 1264200, 1854160, 2469600, 3178560, 11124960, 12566400, 13906200, 22924160, 27812400, 107557632, 120165120, 212385600

Offset

1,1

Comments

The least instances for 4/3, 5/3, 7/3, 8/3, 10/3 and 11/3 are: 4, 20, 14, 672, 3360, 36960.

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

Links

Table of n, a(n) for n=1..35.

Example

4 is a term because 4/A206369(4) = 4/3.
14 is a term because 14/A206369(14) = 14/6 = 7/3.

Mathematica

Select[Range[10^5], Denominator[#/(# DivisorSum[#, LiouvilleLambda[#]/# &])] == 3 &] (* Michael De Vlieger, Dec 29 2017 *)

Prog

(PARI) rhope(p, e) = my(s=1); for(i=1, e, s=s*p + (-1)^i); s;
rho(n) = my(f=factor(n)); prod(i=1, #f~, rhope(f[i, 1], f[i, 2]));
isok(n) = denominator(n/rho(n))==3;

Crossrefs

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

Cf. A245775 (analog for sigma).

Sequence in context: A075319 A030470 A326004 * A267768 A185008 A165721

Adjacent sequences: A297355 A297356 A297357 * A297359 A297360 A297361

Keyword

nonn

Author

Michel Marcus, Dec 29 2017

Extensions

a(33)-a(35) from Jinyuan Wang, Feb 10 2020

Status

approved