A366683 -id:A366683 - cp's OEIS frontend

A366652 Number of divisors of 8^n-1.

2, 6, 4, 24, 8, 32, 12, 96, 8, 96, 16, 512, 16, 144, 64, 768, 32, 160, 16, 4608, 96, 384, 16, 8192, 128, 192, 64, 9216, 64, 4096, 8, 6144, 256, 1536, 1536, 10240, 64, 384, 512, 73728, 32, 6144, 32, 24576, 1024, 384, 64, 262144, 64, 12288, 256, 147456, 256

Offset: 1

Sean A. Irvine, Oct 15 2023

nonn

			a(5)=8 because 8^5-1 has divisors {1, 7, 31, 151, 217, 1057, 4681, 32767}.

Max Alekseyev, Table of n, a(n) for n = 1..500

Cf. A024088, A000005, A057953, A059890, A366651, A366653, A366654.

Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366661, A070528, A366683, A366709.

a:=n->numtheory[tau](8^n-1):
seq(a(n), n=1..100);

Mathematica
```
DivisorSigma[0, 8^Range[100]-1]
```
PARI
```
a(n) = numdiv(8^n-1);
```

a(n) = sigma0(8^n-1) = A000005(A024088(n)).

a(n) = A046801(3*n). - Max Alekseyev, Jan 09 2024

A366575 Number of divisors of 3^n - 1.

Original entry on oeis.org

2, 4, 4, 10, 6, 16, 4, 24, 8, 24, 8, 80, 4, 16, 24, 112, 8, 128, 8, 180, 16, 64, 8, 384, 24, 16, 64, 160, 16, 768, 16, 256, 32, 128, 48, 1280, 8, 64, 96, 864, 16, 768, 8, 640, 384, 32, 32, 14336, 128, 384, 64, 160, 16, 4096, 128, 1536, 128, 256, 8, 23040, 8

Offset: 1

Sean A. Irvine, Oct 13 2023

nonn

			a(4)=10 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Max Alekseyev, Table of n, a(n) for n = 1..690

Cf. A024023, A000005, A046801, A133801, A295500, A366576.

Cf. A046801, A366602, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

a:=n->numtheory[tau](3^n-1):
seq(a(n), n=1..100);

DivisorSigma[0,3^Range[100]-1] (* Paolo Xausa, Oct 15 2023 *)

a(n) = sigma0(3^n-1) = A000005(A024023).

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

A366652 Number of divisors of 8^n-1.

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A366575 Number of divisors of 3^n - 1.

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Author

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Examples

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Crossrefs

Programs

Maple

Mathematica

Formula

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

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula