A266269 -id:A266269 - cp's OEIS frontend

A091439 Least k such that k/phi(k) >= n, where phi is Euler's totient function.

1, 2, 6, 210, 30030, 223092870, 13082761331670030, 3217644767340672907899084554130, 1492182350939279320058875736615841068547583863326864530410, 16516447045902521732188973253623425320896207954043566485360902980990824644545340710198976591011245999110

Offset: 1

T. D. Noe, Jan 09 2004

Max Alekseyev, Table of n, a(n) for n = 1..15
Eric Weisstein's World of Mathematics, Totient Function

Subsequence of A002110.

Cf. A091456 (n * phi(k) < k), A256968, A266269, A266276.

Mathematica
```
Table[prod=1; i=0; While[prod
				
```

a(n) = my(p=1, i=0); while(pMichel Marcus, Oct 07 2019

a(n) = A002110(A256968(n)). - Michel Marcus, Oct 07 2019

A266276 a(n) is the smallest number k such that phi(k) = n*phi(k-1).

Original entry on oeis.org

2, 3, 7, 1261, 11242771

Offset: 1

Jaroslav Krizek, Jan 26 2016

a(n) >= A266269(n). - Max Alekseyev, Jan 26 2025

			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.

Sequences of numbers n such that phi(n) = k*phi(n-1): {A001274 + 1} for k=1; A171271 = {A050472 + 1} for k=2; A266268 = {A067143 + 1} for k=3; A268126 = {A172314 + 1} for k=4; {A201253 + 1} for k=5.

Cf. A000010, A091439, A091456, A266269.

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

a(n) = my(k=2, epk=1, enk); while ((enk=eulerphi(k)) != n*epk, epk = enk; k++); k; \\ Michel Marcus, Feb 20 2020

cp's OEIS Frontend

A091439 Least k such that k/phi(k) >= n, where phi is Euler's totient function.

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