A057939 -id:A057939 - cp's OEIS frontend

A366616 Number of divisors of 5^n+1.

2, 4, 4, 12, 4, 8, 8, 16, 8, 32, 16, 32, 8, 16, 8, 96, 8, 16, 32, 32, 16, 576, 16, 16, 16, 32, 24, 320, 8, 16, 128, 32, 16, 384, 64, 128, 64, 32, 16, 192, 32, 64, 64, 64, 8, 512, 8, 32, 32, 128, 128, 768, 32, 32, 64, 128, 128, 384, 8, 64, 64, 64, 16, 24576, 16

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

			a(3)=12 because 5^3+1 has divisors {1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126}.

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

Cf. A000005, A034474, A057939, A074478, A366612, A366607, A366615, A366617, A366618.

Cf. A046798, A366577, A366606, A366628, A366637, A366656, A366665, A344897, A366688, A366714.

a:=n->numtheory[tau](5^n+1):
seq(a(n), n=0..100);

DivisorSigma[0, 5^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)

PARI
```
a(n) = numdiv(5^n+1);
```

a(n) = sigma0(5^n+1) = A000005(A034474(n)).

A366617 Sum of the divisors of 5^n+1.

Original entry on oeis.org

3, 12, 42, 312, 942, 6264, 25284, 162000, 620460, 4961280, 16161768, 103442688, 367381884, 2441936064, 9859525284, 76963663296, 228970112844, 1526377433328, 6339280635408, 38199227335200, 144103649734968, 1285221510144000, 3894650946433800, 24349131482713344

Offset: 0

Sean A. Irvine, Oct 14 2023

nonn

			a(3)=312 because 5^3+1 has divisors {1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126}.

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

Cf. A000203, A034474, A057939, A074478, A366613, A366615, A366616, A366618.

Cf. A069061, A366578, A366607, A366629, A366638, A366657, A366666, A366668, A366689, A366715.

a:=n->numtheory[sigma](5^n+1):
seq(a(n), n=0..100);

DivisorSigma[1, 5^Range[0, 30] + 1] (* Paolo Xausa, Jul 03 2024 *)

a(n) = sigma(5^n+1) = A000203(A034474(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)).

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 3, 2, 5, 2, 4, 4, 4, 3, 7, 3, 7, 4, 6, 5, 8, 3, 6, 5, 7, 4, 7, 4, 7, 7, 6, 3, 10, 6, 6, 6, 7, 4, 13, 6, 11, 7, 5, 4, 11, 5, 6, 9, 5, 6, 13, 6, 7, 5, 8, 6, 11, 3, 7, 9, 13, 7, 12, 6, 7, 8, 6, 4, 13, 3, 10, 8, 9, 7, 14, 8, 6, 10, 8, 8, 13, 6, 12, 12, 7, 10

Offset: 0

Sean A. Irvine, Oct 16 2023

nonn

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

Cf. A034524, A001222, A057934, A062308, A366686, A366688, A366689, A366690.

Cf. A054992, A057941, A057940, A057939, A057938, A057937, A057936, A057935, A057934, A366713.

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

a(n) = bigomega(11^n+1) = A001222(A034524(n)).

cp's OEIS Frontend

A366616 Number of divisors of 5^n+1.

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A366617 Sum of the divisors of 5^n+1.

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Author

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Programs

Maple

Mathematica

Formula

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

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Crossrefs

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Mathematica

PARI

Formula

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula