A266268 -id:A266268 - cp's OEIS frontend

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

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

A268126 Numbers n such that phi(n) = 4*phi(n-1).

Original entry on oeis.org

1261, 13651, 17557, 18721, 24511, 42121, 113611, 244531, 266071, 712081, 749911, 795691, 992251, 1080721, 1286731, 1458271, 1849471, 2271061, 2457691, 3295381, 3370771, 3414841, 3714751, 4061971, 4736491, 5314051, 5827081, 6566911, 6935083, 7303981, 7864081

Offset: 1

Jaroslav Krizek, Jan 26 2016

nonn

See A266276(n) = the smallest numbers k such that phi(k) = n * phi(k-1) for n >=1: 2, 3, 7, 1261, 11242771, ...

			1261 is in the sequence because phi(1261) = 1152 = 4*phi(1260) = 4*288.

Cf. A000010, A171271 (numbers n such that phi(n) = 2*phi(n-1)), A266268 (numbers n such that phi(n) = 3*phi(n-1)), A266276.

Cf. A256937.

[n: n in [2..10^7] | EulerPhi(n) eq 4*EulerPhi(n-1)]

Select[Range@10000000, EulerPhi@# == 4 EulerPhi[# - 1] &] (* Vincenzo Librandi, Jan 27 2016 *)

isok(n) = (eulerphi(n) == 4*eulerphi(n-1)); \\ Michel Marcus, Jan 27 2016

a(n) = A172314(n) + 1. - Michel Marcus, Jan 27 2016

cp's OEIS Frontend

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

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