A172314 -id:A172314 - cp's OEIS frontend

A067143 Numbers n such that phi(n+1) = 3*phi(n).

6, 12, 18, 36, 72, 90, 96, 108, 162, 192, 432, 486, 576, 702, 768, 792, 924, 1152, 1296, 1458, 2592, 2916, 3456, 3888, 4698, 5550, 6696, 7998, 8700, 10368, 10590, 11802, 12288, 16470, 17496, 18432, 33250, 39366, 52488, 56790, 79248, 124356

Offset: 1

Benoit Cloitre, Feb 19 2002

nonn

Donovan Johnson, Table of n, a(n) for n = 1..1000

Cf. A001274, A050472, A172314.

Position[Partition[EulerPhi[Range[125000]],2,1],?(#[[2]]==3#[[1]]&), 1,Heads-> False]//Flatten (* _Harvey P. Dale, Jul 30 2020 *)

isok(n) = eulerphi(n+1) == 3*eulerphi(n); \\ Michel Marcus, Nov 20 2013

More terms from Dean Hickerson, Feb 20 2002

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

A201253 Numbers k such that phi(k+1) = 5*phi(k).

Original entry on oeis.org

11242770, 18673200, 77805000, 117138840, 122649450, 278023200, 393513120, 881879460, 2177410830, 2364390210, 3440848320, 3919303080, 5151045900, 5836032510, 7284273360, 8029787220, 8505803460, 12998545560, 13081794180, 13759304790, 14031484740, 14104654410

Offset: 1

Ray Chandler, Nov 28 2011

nonn

Giovanni Resta, Table of n, a(n) for n = 1..92 (terms < 10^12)

Cf. A000010, A001274, A050472, A067143, A172314.

isok(k) = eulerphi(k+1) == 5*eulerphi(k); \\ Michel Marcus, Aug 10 2025

a(9)-a(22) from Donovan Johnson, Nov 29 2011

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

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A067143 Numbers n such that phi(n+1) = 3*phi(n).

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

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A201253 Numbers k such that phi(k+1) = 5*phi(k).

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

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