cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 14 results. Next

A366683 Number of divisors of 11^n-1.

Original entry on oeis.org

4, 16, 16, 40, 12, 192, 16, 96, 32, 96, 16, 1920, 16, 128, 96, 448, 8, 1024, 8, 480, 768, 1024, 32, 18432, 128, 512, 64, 2560, 16, 9216, 32, 2048, 512, 256, 192, 20480, 64, 512, 4096, 4608, 512, 36864, 16, 10240, 384, 2048, 32, 1376256, 128, 4096, 512, 2560
Offset: 1

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Examples

			a(3)=16 because 11^3-1 has divisors {1, 2, 5, 7, 10, 14, 19, 35, 38, 70, 95, 133, 190, 266, 665, 1330}.

Links

Crossrefs

Cf. A024127, A000005, A366681, A366682, A366684, A366685.
Cf. A046801, A070528, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](11^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0, 11^Range[100]-1]
  • PARI
    a(n) = numdiv(11^n-1);

Formula

a(n) = sigma0(11^n-1) = A000005(A024127(n)).

A366707 Number of distinct prime divisors of 12^n - 1.

Original entry on oeis.org

1, 2, 2, 4, 2, 5, 3, 6, 4, 4, 3, 8, 3, 6, 6, 9, 3, 9, 2, 7, 5, 5, 4, 12, 4, 7, 6, 10, 5, 13, 5, 11, 7, 6, 9, 14, 3, 6, 7, 13, 4, 13, 5, 11, 12, 8, 3, 18, 5, 10, 6, 12, 7, 16, 7, 13, 7, 8, 4, 18, 4, 8, 8, 13, 8, 16, 5, 10, 7, 14, 4, 21, 3, 7, 11, 11, 10, 17, 4
Offset: 1

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A024140, A001221, A046800, A133801, A102347, A250288, A252170, A366708, A366709, A366681.

Programs

  • PARI
    for(n = 1, 100, print1(omega(12^n - 1), ", "))

Formula

a(n) = omega(12^n-1) = A001221(A024140(n)).

A366714 Number of divisors of 12^n+1.

Original entry on oeis.org

2, 2, 4, 8, 4, 4, 8, 8, 8, 32, 12, 4, 16, 24, 16, 128, 4, 8, 32, 16, 64, 384, 64, 16, 64, 64, 32, 1024, 8, 8, 48, 8, 4, 512, 16, 32, 128, 16, 32, 1536, 16, 32, 64, 32, 16, 4096, 8, 32, 32, 32, 512, 512, 32, 32, 1024, 128, 512, 1536, 192, 64, 1024, 32, 64
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Examples

			a(4)=4 because 12^4+1 has divisors {1, 89, 233, 20737}.

Links

Crossrefs

Cf. A178248, A000005, A046798, A344897, A366709, A366712, A366713, A366715, A366716, A366719, A366720, A366688.

Programs

  • Maple
    a:=n->numtheory[tau](12^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 12^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)
  • PARI
    a(n) = numdiv(12^n+1);

Formula

a(n) = sigma0(12^n+1) = A000005(A178248(n)).

A366710 Sum of the divisors of 12^n-1.

Original entry on oeis.org

12, 168, 1896, 30240, 271464, 4247040, 39156480, 636854400, 5817876000, 72749094432, 852203639280, 15743437516800, 116720110574544, 1518251476008960, 17220536137159296, 292933954031846400, 2420303924088730368, 38936041113123840000, 348523635677043192936
Offset: 1

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Examples

			a(3)=1896 because 12^3-1 has divisors {1, 11, 157, 1727}.

Links

Crossrefs

Cf. A024140, A000203, A366707, A366708, A366709, A366711, A366684.

Programs

  • Maple
    a:=n->numtheory[sigma](12^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 12^Range[30]-1]

Formula

a(n) = sigma(12^n-1) = A000203(A024140(n)).

A366711 a(n) = phi(12^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

10, 120, 1560, 13440, 226200, 2021760, 32518360, 274391040, 4534807680, 51953616000, 646094232960, 4662793175040, 97266341877120, 1070382142166400, 13666309113600000, 109897747141754880, 2016918439151095000, 17518491733377024000, 290436363064202660760
Offset: 1

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), A366623 (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), this sequence (k=12).
Cf. A000010, A024140, A366707, A366708, A366709, A366710, A366717, A366718.

Programs

  • Mathematica
    EulerPhi[12^Range[30] - 1]
  • PARI
    {a(n) = eulerphi(12^n-1)}

A366621 Number of divisors of 6^n-1.

Original entry on oeis.org

2, 4, 4, 8, 6, 16, 4, 16, 16, 48, 8, 128, 8, 48, 48, 64, 32, 128, 8, 384, 16, 32, 32, 512, 32, 128, 64, 384, 4, 1536, 8, 512, 64, 256, 96, 8192, 64, 64, 64, 3072, 8, 768, 32, 512, 1536, 256, 16, 8192, 32, 512, 512, 2048, 16, 2048, 96, 12288, 128, 64, 16
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(4)=8 because 6^4-1 has divisors {1, 5, 7, 35, 37, 185, 259, 1295}.

Links

Crossrefs

Cf. A024062, A000005, A057955, A059888, A274907, A366613, A366620, A366622, A366623.
Cf. A046801, A366575, A366602, A366612, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](6^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0, 6^Range[100]-1]
  • PARI
    a(n) = numdiv(6^n-1);

Formula

a(n) = sigma0(6^n-1) = A000005(A024062(n)).

A366661 Number of divisors of 9^n-1.

Original entry on oeis.org

4, 10, 16, 24, 24, 80, 16, 112, 128, 180, 64, 384, 16, 160, 768, 256, 128, 1280, 64, 864, 768, 640, 32, 14336, 384, 160, 4096, 1536, 256, 23040, 128, 576, 2048, 1280, 768, 12288, 128, 640, 12288, 16128, 128, 61440, 32, 12288, 196608, 320, 512, 131072, 2048
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(2)=10 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Links

Crossrefs

Cf. A024101, A000005, A057952, A366660, A366662, A366663.
Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366652, A070528, A366683, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](9^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0, 9^Range[100]-1]
  • PARI
    a(n) = numdiv(9^n-1);

Formula

a(n) = sigma0(9^n-1) = A000005(A024101(n)).
a(n) = A366575(2*n) = A366575(n) * A366577(n) * (4 + A007814(n)) / (2 * (3 + A007814(n))). - Max Alekseyev, Jan 07 2024

A366602 Number of divisors of 4^n-1.

Original entry on oeis.org

2, 4, 6, 8, 8, 24, 8, 16, 32, 48, 16, 96, 8, 64, 96, 32, 8, 512, 8, 192, 144, 128, 16, 768, 128, 128, 160, 256, 64, 4608, 8, 128, 384, 128, 512, 8192, 32, 128, 192, 768, 32, 9216, 32, 1024, 4096, 512, 64, 6144, 32, 8192, 1536, 1024, 64, 10240, 3072, 2048, 384
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(4)=8 because 4^4-1 has divisors {1, 3, 5, 15, 17, 51, 85, 255}.

Links

Crossrefs

Cf. A024036, A000005, A057957, A295501, A366603, A366604.
Cf. A046798, A046801, A366575, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](4^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0,4^Range[100]-1] (* Paolo Xausa, Oct 14 2023 *)
  • PARI
    a(n) = numdiv(4^n-1);

Formula

a(n) = sigma0(4^n-1) = A000005(A024036(n)).
a(n) = A046801(2*n) = A046798(n) * A046801(n). - Max Alekseyev, Jan 07 2024

A366633 Number of divisors of 7^n-1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A024075, A000005, A057954, A059889, A074249, A218358, A366632, A366634, A366635.
Cf. A046801, A366575, A366602, A366612, A366621, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    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);

Formula

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

A366612 Number of divisors of 5^n-1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A024049, A000005, A057956, A059887, A074479, A143665, A295502, A218357, A366611, A366613.
Cf. A046801, A366575, A366602, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    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);

Formula

a(n) = sigma0(5^n-1) = A000005(A024049(n)).
Showing 1-10 of 14 results. Next

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