A366687 -id:A366687 - cp's OEIS frontend

A366690 a(n) = phi(11^n+1), where phi is Euler's totient function (A000010).

1, 4, 60, 432, 7320, 53680, 803520, 6495720, 100874752, 764738496, 12756110400, 89493288192, 1568774615040, 11278053084480, 180228847518720, 1310982643872000, 22974417331646464, 168479281019744640, 2521788545778163200, 20190830281379049600

Offset: 0

Sean A. Irvine, Oct 16 2023

nonn

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

Cf. A034524, A000010, A062308, A366685, A366686, A366687, A366689, A366689, A366716.

EulerPhi[11^Range[0,19] + 1] (* Paul F. Marrero Romero, Nov 10 2023 *)

PARI
```
{a(n) = eulerphi(11^n+1)}
```

a(n) = A000010(A034524(n)). - Paul F. Marrero Romero, Nov 10 2023

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)).

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)).

A366713 Number of prime factors of 12^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 1, 2, 3, 2, 2, 3, 3, 3, 5, 4, 2, 4, 5, 4, 7, 2, 3, 5, 4, 6, 9, 6, 4, 6, 6, 5, 10, 3, 3, 6, 3, 2, 9, 4, 5, 7, 4, 5, 11, 4, 5, 6, 5, 4, 12, 3, 5, 5, 5, 10, 9, 5, 5, 10, 7, 9, 11, 8, 6, 10, 5, 6, 15, 5, 9, 11, 4, 5, 12, 10, 3, 10, 5, 8, 17, 5, 6, 9, 4, 6, 15

Offset: 0

Sean A. Irvine, Oct 17 2023

nonn

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

Cf. A178248, A001222, A054992, A057934, A057935, A057936, A057937, A057938, A057939, A057940, A057941, A366712, A366714, A366715, A366716, A366719, A366720, A366708, A366687.

Mathematica
```
PrimeOmega[12^Range[70]+1]
```
PARI
```
a(n)=bigomega(12^n+1)
```

a(n) = bigomega(12^n+1) = A001222(A178248(n)).

A366682 Number of prime factors of 11^n - 1 (counted with multiplicity).

Original entry on oeis.org

2, 5, 4, 7, 4, 9, 4, 9, 5, 8, 4, 13, 4, 8, 7, 12, 3, 12, 3, 11, 10, 11, 5, 17, 8, 10, 6, 13, 4, 15, 5, 15, 9, 9, 8, 17, 6, 10, 12, 15, 9, 17, 4, 15, 9, 12, 5, 24, 7, 14, 9, 13, 6, 16, 10, 19, 8, 10, 5, 21, 5, 12, 16, 19, 8, 22, 6, 15, 10, 19, 7, 24, 3, 11, 15

Offset: 1

Sean A. Irvine, Oct 16 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..316

Cf. A024127, A001222, A366681, A366683, A366684, A366685, A366687.

Cf. A046051, A057958, A057957, A057956, A057955, A057954, A057953, A057952, A057951, A366708.

Mathematica
```
PrimeOmega[11^Range[70]-1]
```
PARI
```
a(n)=bigomega(11^n-1)
```

a(n) = bigomega(11^n-1) = A001222(A024127(n)).

cp's OEIS Frontend

A366690 a(n) = phi(11^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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PARI

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

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Maple

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A366688 Number of divisors of 11^n+1.

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Maple

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A366713 Number of prime factors of 12^n + 1 (counted with multiplicity).

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A366682 Number of prime factors of 11^n - 1 (counted with multiplicity).

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Mathematica

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Formula