A295502 -id:A295502 - cp's OEIS frontend

A366612 Number of divisors of 5^n-1.

3, 8, 6, 20, 12, 48, 6, 48, 24, 64, 6, 240, 6, 64, 96, 224, 12, 512, 24, 640, 48, 128, 12, 1152, 192, 64, 384, 320, 24, 6144, 12, 1024, 48, 128, 384, 10240, 24, 512, 48, 6144, 12, 18432, 12, 1280, 3072, 128, 6, 10752, 12, 4096, 192, 960, 24, 81920, 576, 1536

Offset: 1

Sean A. Irvine, Oct 14 2023

nonn

			a(3)=6 because 5^3-1 has divisors {1, 2, 4, 31, 62, 124}.

Max Alekseyev, Table of n, a(n) for n = 1..502

Cf. A024049, A000005, A057956, A059887, A074479, A143665, A295502, A218357, A366611, A366613.

Cf. A046801, A366575, A366602, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

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

Mathematica
```
DivisorSigma[0, 5^Range[100]-1]
```
PARI
```
a(n) = numdiv(5^n-1);
```

a(n) = sigma0(5^n-1) = A000005(A024049(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)}
```

A366611 Number of distinct prime divisors of 5^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 2, 4, 4, 5, 2, 6, 2, 5, 6, 6, 3, 7, 4, 8, 5, 6, 3, 8, 7, 5, 8, 7, 4, 11, 3, 8, 5, 6, 8, 11, 4, 8, 5, 11, 3, 12, 3, 9, 11, 6, 2, 11, 3, 11, 7, 8, 4, 14, 8, 9, 6, 7, 3, 17, 4, 7, 10, 11, 7, 12, 6, 11, 8, 14, 3, 16, 4, 8, 15, 11, 6, 11, 4, 15

Offset: 1

Sean A. Irvine, Oct 14 2023

nonn

Max Alekseyev, Table of n, a(n) for n = 1..502

Cf. A024049, A001221, A057956, A059887, A074479, A143665, A218357, A295502, A366612, A366613.

Cf. A046800, A133801, A366604, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

for(n = 1, 100, print1(omega(5^n - 1), ", "))

a(n) = omega(5^n-1) = A001221(A024049(n)).

cp's OEIS Frontend

A366612 Number of divisors of 5^n-1.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

A366611 Number of distinct prime divisors of 5^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula