A257865 Smallest k such that phi(k) = n*phi(k+1), where phi(n) = A000010(n) gives the value of Euler's totient function at n.

1, 5, 119, 629, 17907119

Offset: 1

Author

Felix Fröhlich, May 11 2015

Keywords

• nonn
• more

Comments

From Manfred Scheucher, May 27 2015: (Start)

a(6)>=3*10^8 (calculation)

a(7)>=3.5*10^13, a(8)>=4.5*10^25, a(9)>=3.0*10^47, and so on... (doubly exponential lower bound, see uploaded pdf)

239719159679 and 239742643139 admit a ratio of 5.998... and 6.008..., resp.

There might be a relation to the sequence A098026. (End)

Examples

			a(3) = 119, because phi(119) == 3*phi(120) = 96 and 119 is the smallest k where this equality holds for n = 3.
		

Links

• Manfred Scheucher, A lower bound on A257865(n)

Crossrefs

Cf. A001274, A171262, A256907, A256937, A257550.

Programs

Mathematica

Table[k = 1; While[EulerPhi[k] != n EulerPhi[k + 1], k++]; k, {n, 4}] (* Michael De Vlieger, May 12 2015 *)

PARI

a(n) = my(k=1); while(eulerphi(k)!=n*eulerphi(k+1), k++); k

Formula

a(n) >= exp(exp(c(n-3))) with c=exp(gamma) and gamma being the Euler-Mascheroni_constant (see pdf). - Manfred Scheucher, May 27 2015