A348159 Indices k of records of low value in the ratios A348158(k)/k.

1, 2, 126, 1638, 2394, 8190, 139230, 155610, 2645370, 5757570, 97878690, 420302610, 1963331370, 7145144370

Offset: 1

Author

Amiram Eldar, Oct 03 2021

Keywords

• nonn
• more

Comments

The maximal possible value of the ratio A348158(k)/k is 1 which occurs at the terms of A326835.

The rounded values of the corresponding records are 1, 0.5, 0.452, 0.445, 0.437, 0.424, 0.420, 0.409, 0.404, 0.398, 0.3933, 0.3927, 0.3885, 0.3879, ...

a(15) <= 33376633290. - David A. Corneth, Oct 04 2021

Crossrefs

Cf. A326835, A328859, A348158.

Programs

Mathematica

r[n_] := Plus @@ DeleteDuplicates @ Map[EulerPhi, Divisors[n]]/n; rm = 2; s = {}; Do[If[(r1 = r[n]) < rm, rm = r1; AppendTo[s, n]], {n, 1, 2*10^5}]; s

PARI

f(n) = vecsum(Set(apply(eulerphi, divisors(n)))); \\ A348158
lista(nn) = {my(r=oo, x); for (i=1, nn, if ((x=f(i)/i) < r, print1(i, ", "); r = x););} \\ Michel Marcus, Oct 04 2021