A342867 a(n) is the least number k such that the continued fraction for phi(k)/k contains exactly n elements.

1, 2, 3, 15, 35, 33, 65, 215, 221, 551, 455, 2001, 3417, 3621, 11523, 16705, 16617, 69845, 107545, 157285, 324569, 358883, 1404949, 1569295, 3783970, 3106285, 7536065, 12216295, 10589487, 24038979, 57759065, 51961945, 177005465, 131462695, 741703701, 1467144445

Offset: 1

Author

Amiram Eldar, Mar 27 2021

Keywords

• nonn

Comments

a(n) is the least number k such that A342866(k) = n.

All the terms above 3 are composite numbers.

Crossrefs

Cf. A000010, A007694, A076512, A109395, A342866.

Cf. A071865 (similar, with sigma(k)/k).

Programs

Mathematica

f[n_] := Length @ ContinuedFraction[EulerPhi[n]/n]; seq[max_] := Module[{s = Table[0, {max}], c = 0, n  = 1, i}, While[c < max, i = f[n]; If[i <= max && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[20]

PARI

a(n) = my(k=1); while (#contfrac(eulerphi(k)/k) != n, k++); k; \\ Michel Marcus, Mar 30 2021

Formula

a(2) = 2 since 2 is the least number k such that A342866(k) = 2.