A366690 -id:A366690 - cp's OEIS frontend

A366716 a(n) = phi(12^n+1), where phi is Euler's totient function (A000010).

1, 12, 112, 1296, 20416, 229680, 2306304, 32916240, 400515072, 3863116800, 47825825600, 685853880624, 8732596764672, 97509650382144, 990242755633152, 11148606564480000, 184883057981234176, 2047145911595946000, 20281543142263603200, 294779525244632305920

Offset: 0

Sean A. Irvine, Oct 17 2023

nonn

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

Cf. A178248, A000010, A366711, A366712, A366713, A366714, A366715, A366719, A366720, A366690.

EulerPhi[12^Range[0,19] + 1] (* Paul F. Marrero Romero, Oct 27 2023 *)

PARI
```
{a(n) = eulerphi(12^n+1)}
```

a(n) = A000010(A178248(n)). - Paul F. Marrero Romero, Oct 27 2023

A366608 a(n) = phi(4^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 16, 48, 256, 800, 3840, 12544, 65536, 186624, 986880, 3345408, 16515072, 52306176, 252645120, 760320000, 4288266240, 13628740608, 64258375680, 218462552064, 1095233372160, 3105655160832, 16510446886912, 56000724240384, 280012271910912, 869940000000000

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..583

Cf. A000010, A052539, A057940, A274903, A295501, A366605, A366606, A366607, A366609.

Cf. A053285, A366579, A366618, A366630, A366639, A366658, A366667, A366669, A366690, A366716.

EulerPhi[4^Range[0,30]+1] (* Paolo Xausa, Oct 14 2023 *)

PARI
```
{a(n) = eulerphi(4^n+1)}
```

from sympy import totient
def A366608(n): return totient((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

a(n) = A053285(2*n). - Max Alekseyev, Jan 08 2024

A366686 Number of distinct prime divisors of 11^n + 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 4, 3, 3, 4, 3, 6, 4, 5, 5, 6, 3, 5, 5, 6, 4, 5, 4, 6, 7, 5, 3, 6, 6, 5, 6, 6, 4, 11, 6, 9, 7, 4, 4, 9, 5, 5, 9, 4, 6, 10, 6, 6, 5, 7, 6, 9, 3, 6, 9, 12, 7, 10, 6, 6, 8, 5, 4, 10, 3, 9, 8, 8, 7, 12, 8, 5, 10, 7, 8, 11, 6, 11, 11, 6, 10, 9, 5

Offset: 0

Sean A. Irvine, Oct 16 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..325

Cf. A034524, A001221, A366681, A102347, A366687, A366688, A366689, A366690.

Cf. A046799, A119704, A366712.

for(n = 0, 100, print1(omega(11^n + 1), ", "))

a(n) = omega(11^n+1) = A001221(A034524(n)).

A366689 Sum of the divisors of 11^n+1.

Original entry on oeis.org

3, 28, 186, 3458, 21966, 375816, 2911272, 45470096, 340452396, 6278429920, 39543942612, 706019328000, 4708961513592, 82162955169792, 599236951715280, 11195197038864384, 68925937595777100, 1179397832668228992, 9136813499663186064, 144079834776308121600

Offset: 0

Sean A. Irvine, Oct 16 2023

nonn

			a(4)=21966 because 11^4+1 has divisors {1, 2, 7321, 14642}.

Max Alekseyev, Table of n, a(n) for n = 0..325

Cf. A034524, A000203, A366666, A366684, A366686, A366687, A366688, A366690, A366715.

a:=n->numtheory[sigma](11^n+1):
seq(a(n), n=0..100);

DivisorSigma[1,11^Range[0,20]+1] (* Harvey P. Dale, Jun 22 2025 *)

a(n) = sigma(11^n+1) = A000203(A034524(n)).

A366630 a(n) = phi(6^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 6, 36, 180, 1296, 6000, 41472, 230496, 1580800, 8359200, 58579200, 310968900, 2175102720, 10971642240, 76065091200, 351048600000, 2811459796992, 14508487949472, 88870766837760, 522016066337712, 3564233663616000, 17479898551382400, 128060205344805888

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..430

Cf. A062394, A000010, A366623, A366618, A366627, A366628, A366629, A366670.

Cf. A053285, A366579, A366608, A366639, A366658, A366667, A366669, A366690, A366716.

EulerPhi[6^Range[0, 22] + 1] (* Paul F. Marrero Romero, Oct 17 2023 *)

PARI
```
{a(n) = eulerphi(6^n+1)}
```

a(n) = A000010(A062394(n)). - Paul F. Marrero Romero, Oct 17 2023

A366667 a(n) = phi(9^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 40, 288, 3072, 23600, 259200, 1847104, 21523360, 152845056, 1700870400, 12550120000, 130459631616, 997562438080, 11159367815680, 81159501312000, 926510094425920, 6670865700716544, 73205598106368000, 540340585126398016, 5691215305506816000

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..345

Cf. A062396, A000010, A366663, A366664, A366665, A366666.

Cf. A053285, A366579, A366608, A366618, A366630, A366639, A366658, A366669, A366690, A366716.

EulerPhi[9^Range[0, 20] + 1] (* Paul F. Marrero Romero, Nov 04 2023 *)

PARI
```
{a(n) = eulerphi(9^n+1)}
```

a(n) = A000010(A062396(n)). - Paul F. Marrero Romero, Nov 04 2023

a(n) = A366579(2*n). - Max Alekseyev, Jan 08 2024

A366688 Number of divisors of 11^n+1.

Original entry on oeis.org

2, 6, 4, 18, 4, 12, 16, 12, 8, 48, 8, 96, 16, 48, 32, 144, 8, 48, 32, 96, 16, 72, 16, 96, 128, 48, 8, 240, 64, 48, 64, 96, 16, 4608, 64, 1152, 128, 24, 16, 1152, 32, 48, 512, 24, 64, 3072, 64, 96, 32, 192, 64, 1152, 8, 96, 512, 6144, 128, 2304, 64, 96, 256, 48

Offset: 0

Sean A. Irvine, Oct 16 2023

nonn

			a(4)=4 because 11^4+1 has divisors {1, 2, 7321, 14642}.

Max Alekseyev, Table of n, a(n) for n = 0..325

Cf. A034524, A000005, A062308, A366683, A366686, A366687, A366689, A366690.

Cf. A046798, A344897, A366714.

a:=n->numtheory[tau](11^n+1):
seq(a(n), n=0..100);

DivisorSigma[0,11^Range[0,70]+1] (* Harvey P. Dale, Mar 17 2025 *)

PARI
```
a(n) = numdiv(11^n+1);
```

a(n) = sigma0(11^n+1) = A000005(A034524(n)).

A366618 a(n) = phi(5^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 2, 12, 36, 312, 1040, 7200, 25088, 183808, 557928, 4396800, 15333120, 121680000, 406812744, 2817007200, 8558784000, 76264519680, 254230063200, 1710194342400, 6349120596480, 47334145996800, 127169887444992, 1088029470747648, 3889097389599864

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..471

Cf. A000010, A034474, A057939, A074478, A295502, A366615, A366616, A366617.

Cf. A053285, A366579, A366608, A366630, A366639, A366658, A366667, A366669, A366690, A366716.

EulerPhi[5^Range[0,30]+1] (* Harvey P. Dale, Jun 07 2025 *)

PARI
```
{a(n) = eulerphi(5^n+1)}
```

A366639 a(n) = phi(7^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 4, 20, 168, 1200, 7600, 43200, 407680, 2712832, 19707408, 112560000, 945677920, 6768230400, 47530457728, 271289229120, 2096760960000, 16569393144832, 116315256993600, 597938524646400, 5699431359135360, 38890647857280000, 270061302781670400

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..387

Cf. A034491, A000010, A057937, A227575, A366635, A366636, A366637, A366638.

Cf. A053285, A366579, A366608, A366618, A366630, A366658, A366667, A366669, A366690, A366716.

EulerPhi[7^Range[0,21] + 1] (* Paul F. Marrero Romero, Nov 05 2023 *)

PARI
```
{a(n) = eulerphi(7^n+1)}
```

a(n) = A000010(A034491(n)). - Paul F. Marrero Romero, Nov 06 2023

A366658 a(n) = phi(8^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 6, 48, 324, 3840, 19800, 186624, 1365336, 16515072, 84768120, 760320000, 5632621632, 64258375680, 366369658200, 3105655160832, 20140520400000, 280012271910912, 1495522910085120, 12824556668190720, 95907982079387520, 1080582572777472000, 5688765822212629632

Offset: 0

Sean A. Irvine, Oct 15 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 0..502

Cf. A062395, A000010, A057936, A274905, A366654, A366655, A366656, A366657, A366671.

Cf. A053285, A366579, A366608, A366618, A366630, A366639, A366667, A366669, A366690, A366716.

EulerPhi[8^Range[0, 21] + 1] (* Paul F. Marrero Romero, Oct 17 2023 *)

PARI
```
{a(n) = eulerphi(8^n+1)}
```

from sympy import totient
def A366658(n): return totient((1<<3*n)+1) # Chai Wah Wu, Oct 15 2023

a(n) = A000010(A062395(n)). - Paul F. Marrero Romero, Nov 06 2023

a(n) = A053285(3*n). - Max Alekseyev, Jan 09 2024

cp's OEIS Frontend

A366716 a(n) = phi(12^n+1), where phi is Euler's totient function (A000010).

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A366608 a(n) = phi(4^n+1), where phi is Euler's totient function (A000010).

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A366686 Number of distinct prime divisors of 11^n + 1.

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A366689 Sum of the divisors of 11^n+1.

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Maple

Mathematica

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A366630 a(n) = phi(6^n+1), where phi is Euler's totient function (A000010).

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Formula

A366667 a(n) = phi(9^n+1), where phi is Euler's totient function (A000010).

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Mathematica

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Formula

A366688 Number of divisors of 11^n+1.

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Maple

Mathematica

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Formula

A366618 a(n) = phi(5^n+1), where phi is Euler's totient function (A000010).

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