A366635 -id:A366635 - cp's OEIS frontend

A366633 Number of divisors of 7^n-1.

4, 10, 12, 36, 8, 60, 16, 84, 64, 80, 16, 864, 8, 160, 96, 384, 16, 640, 16, 1536, 96, 160, 32, 16128, 32, 80, 1280, 1152, 32, 3840, 32, 1728, 384, 80, 128, 18432, 32, 160, 192, 14336, 32, 7680, 16, 4608, 2048, 160, 16, 147456, 256, 640, 768, 1152, 32, 25600

Offset: 1

Sean A. Irvine, Oct 14 2023

nonn

			a(5)=8 because 7^5-1 has divisors {1, 2, 3, 6, 2801, 5602, 8403, 168061}.

Max Alekseyev, Table of n, a(n) for n = 1..388

Cf. A024075, A000005, A057954, A059889, A074249, A218358, A366632, A366634, A366635.

Cf. A046801, A366575, A366602, A366612, A366621, A366652, A366661, A070528, A366683, A366709.

a:=n->numtheory[tau](7^n-1):
seq(a(n), n=1..100);

Mathematica
```
DivisorSigma[0, 7^Range[100]-1]
```
PARI
```
a(n) = numdiv(7^n-1);
```

a(n) = sigma0(7^n-1) = A000005(A024075(n)).

A366634 Sum of the divisors of 7^n-1.

Original entry on oeis.org

12, 124, 780, 7812, 33624, 354640, 1704240, 18929096, 97036800, 800520192, 3958188480, 56928231360, 193778020824, 1830926384640, 11181115146240, 115997032277280, 465294239722800, 5175558387507200, 22852200371636160, 287850454432579584, 1318081737957660000

Offset: 1

Sean A. Irvine, Oct 14 2023

nonn

			a(5)=33624 because 7^5-1 has divisors {1, 2, 3, 6, 2801, 5602, 8403, 16806}.

Max Alekseyev, Table of n, a(n) for n = 1..388

Cf. A024075, A000203, A057954, A059887, A074249, A218358, A366632, A366633, A366635.

Cf. A075708, A366576, A366603, A366613, A366622, A366653, A366662, A102146, A366684, A366710.

a:=n->numtheory[sigma](7^n-1):
seq(a(n), n=1..100);

Mathematica
```
DivisorSigma[1, 7^Range[30]-1]
```

a(n) = sigma(7^n-1) = A000203(A024075(n)).

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

cp's OEIS Frontend

A366633 Number of divisors of 7^n-1.

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A366634 Sum of the divisors of 7^n-1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Formula

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

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Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula