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 11 results. Next

A366623 a(n) = phi(6^n-1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

4, 24, 168, 864, 6200, 30240, 223944, 1119744, 7457184, 37200000, 277618528, 1254113280, 10445497920, 51618196224, 365601600000, 1770091315200, 13439285266176, 62336092492800, 484935499902880, 2179146240000000, 17141125020596640, 86330728271779200
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

phi(k^n-1): A053287 (k=2), A295500 (k=3), A295501 (k=4), A295502 (k=5), this sequence (k=6), A366635 (k=7), A366654 (k=8), A366663 (k=9), A295503 (k=10), A366685 (k=11), A366711 (k=12).
Cf. A024062, A000010, A295502, A366620, A366621, A366622.

Programs

  • Mathematica
    EulerPhi[6^Range[22] - 1] (* Paul F. Marrero Romero, Oct 23 2023 *)
  • PARI
    {a(n) = eulerphi(6^n-1)}

Formula

a(n) = A000010(A024062(n)). - Paul F. Marrero Romero, Oct 23 2023

A366622 Sum of the divisors of 6^n-1.

Original entry on oeis.org

6, 48, 264, 1824, 9672, 67584, 335928, 2367552, 13031040, 94708224, 454285152, 3523559424, 15677418768, 113738502240, 599516366592, 4210539708672, 20465720064000, 154928015278080, 735060126170880, 5906693566844928, 26937015875831424, 188358079273592832
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(4)=1824 because 6^4-1 has divisors {1, 5, 7, 35, 37, 185, 259, 1295}.

Links

Crossrefs

Cf. A024062, A000203, A057955, A059888, A274907, A366620, A366621, A366623, A366629.
Cf. A075708, A366576, A366603, A366613, A366634, A366653, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](6^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 6^Range[30]-1]

Formula

a(n) = sigma(6^n-1) = A000203(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

A366620 Number of distinct prime divisors of 6^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 4, 2, 4, 4, 5, 3, 7, 3, 5, 5, 6, 5, 7, 3, 8, 4, 5, 5, 9, 4, 7, 6, 8, 2, 10, 3, 9, 6, 8, 6, 13, 6, 6, 6, 11, 3, 9, 5, 9, 10, 8, 4, 13, 5, 8, 9, 11, 4, 11, 6, 13, 7, 6, 4, 19, 4, 5, 10, 12, 8, 12, 3, 11, 8, 16, 2, 18, 5, 10, 10, 9, 6, 15, 4, 16, 8
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024062, A001221, A057955, A059888, A274907, A366621, A366622, A366623.
Cf. A046800, A133801, A366604, A366611, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(6^n - 1), ", "))

Formula

a(n) = omega(6^n-1) = A001221(A024062(n)).

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)).

A274907 Largest prime factor of 6^n - 1.

Original entry on oeis.org

5, 7, 43, 37, 311, 43, 55987, 1297, 2467, 311, 3154757, 97, 760891, 55987, 1201, 98801, 30839, 46441, 638073026189, 6781, 1822428931, 51828151, 7505944891, 1678321, 40185601, 760891, 623067280651, 5030761, 7369130657357778596659, 1950271, 49744740983476472807
Offset: 1

Views

Author

Vincenzo Librandi, Jul 11 2016

Keywords

Examples

			6^5 - 1 = 7775 = 5*5*311, so a(5) = 311.

Links

Crossrefs

Cf. A006530, A057955, A059888, A085031, A024062, A366620, A366621, A366622, A366623.
Cf. similar sequences listed in A274906.

Programs

  • Magma
    [Maximum(PrimeDivisors(6^n-1)): n in [1..40]];
  • Mathematica
    Table[FactorInteger[6^n - 1][[-1, 1]], {n, 40}]
  • PARI
    a(n) = vecmax(factor(6^n-1)[,1]); \\ Michel Marcus, Jul 13 2016

Formula

a(n) = A006530(A024062(n)). - Michel Marcus, Jul 11 2016

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)).

A366652 Number of divisors of 8^n-1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A024088, A000005, A057953, A059890, A366651, A366653, A366654.
Cf. A046801, A366575, A366602, A366612, A366621, A366633, A366661, A070528, A366683, A366709.

Programs

  • Maple
    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);

Formula

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

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A024023, A000005, A046801, A133801, A295500, A366576.
Cf. A046801, A366602, A366612, A366621, A366633, A366652, A366661, A070528, A366683, A366709.

Programs

  • Maple
    a:=n->numtheory[tau](3^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[0,3^Range[100]-1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma0(3^n-1) = A000005(A024023).
Showing 1-10 of 11 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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