A366718 -id:A366718 - cp's OEIS frontend

A366711 a(n) = phi(12^n-1), where phi is Euler's totient function (A000010).

10, 120, 1560, 13440, 226200, 2021760, 32518360, 274391040, 4534807680, 51953616000, 646094232960, 4662793175040, 97266341877120, 1070382142166400, 13666309113600000, 109897747141754880, 2016918439151095000, 17518491733377024000, 290436363064202660760

Offset: 1

Sean A. Irvine, Oct 17 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..310

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), this sequence (k=12).

Cf. A000010, A024140, A366707, A366708, A366709, A366710, A366717, A366718.

Mathematica
```
EulerPhi[12^Range[30] - 1]
```
PARI
```
{a(n) = eulerphi(12^n-1)}
```

A366720 Largest prime factor of 12^n+1.

Original entry on oeis.org

2, 13, 29, 19, 233, 19141, 20593, 13063, 260753, 1801, 85403261, 57154490053, 2227777, 222379, 13156924369, 35671, 1200913648289, 66900193189411, 122138321401, 905265296671, 67657441, 1885339, 68368660537, 49489630860836437, 592734049, 438472201

Offset: 0

Sean A. Irvine, Oct 17 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..306

Cf. A178248, A006530, A002587, A074476, A274903, A074478, A274904, A227575, A274905, A002592, A003021, A062308, A002590, A366712, A366713, A366714, A366715, A366716, A366717, A366718, A366719, A324941.

Table[FactorInteger[12^n + 1][[-1, 1]], {n, 0, 20}]

a(n) = A006530(A178248(n)). - Paul F. Marrero Romero, Dec 07 2023

A366717 Smallest prime dividing 12^n - 1.

Original entry on oeis.org

11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5, 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11

Offset: 1

Sean A. Irvine, Oct 17 2023

nonn

Periodic with period 12, repeat of 11, 11, 11, 5, 11, 7, 11, 5, 11, 11, 11, 5.

Cf. A024140, A366718, A366719.

Table[FactorInteger[12^n - 1][[1,1]], {n,71}] (* Paul F. Marrero Romero, Oct 25 2023 *)

a(n) = A020639(A024140(n)). - Paul F. Marrero Romero, Oct 25 2023

cp's OEIS Frontend

A366711 a(n) = phi(12^n-1), where phi is Euler's totient function (A000010).

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PARI

A366720 Largest prime factor of 12^n+1.

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A366717 Smallest prime dividing 12^n - 1.

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Mathematica

Formula