A266269 a(n) is the smallest number k such that phi(k) >= n*phi(k-1).

2, 3, 7, 211, 30031, 223092871, 13082761331670031, 3217644767340672907899084554131, 1492182350939279320058875736615841068547583863326864530411, 16516447045902521732188973253623425320896207954043566485360902980990824644545340710198976591011245999111

Offset: 1

Author

Jaroslav Krizek, Jan 26 2016

Keywords

• nonn

Comments

For the known terms, we have a(n) = 1 + A002110(A256968(n)) = 1 + A091439(n), which likely holds for most (if not all) terms overall. - Max Alekseyev, Jan 26 2025

Examples

			a(3) = 7 because 7 is the smallest number k such that phi(k) >= n*phi(k-1); phi(7) = 6 >= 3*phi(6) = 3*2.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..12

Crossrefs

Cf. A000010, A002110, A091439, A091456, A256968, A266276.

Programs

Magma

a:=func; [a(n):n in[1..5]];

PARI

a(n) = {my(k=2, e=1); while(n*e > e=eulerphi(k), k++); k; } \\ Jinyuan Wang, Nov 01 2020

Extensions

a(6)-a(8) from Jinyuan Wang, Nov 01 2020

a(9)-a(10) from Max Alekseyev, Jan 25 2025