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 10 results.

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)).

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)).

A366653 Sum of the divisors of 8^n-1.

Original entry on oeis.org

8, 104, 592, 8736, 38912, 473600, 2466048, 38054016, 155493536, 2015330304, 10359014400, 166290432000, 636328345600, 7645340651520, 42424026529792, 648494317126656, 2599936977797120, 32817383473149440, 164708609085669376, 3010983668199456768
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(5)=38912 because 8^5-1 has divisors {1, 7, 31, 151, 217, 1057, 4681, 32767}.

Links

Crossrefs

Cf. A024088, A000203, A057953, A059890, A366651, A366652, A366654.
Cf. A075708, A366576, A366603, A366613, A366622, A366634, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](8^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 8^Range[30]-1]
  • SageMath
    [sigma(8**n-1, 1) for n in range(1, 21)] # Stefano Spezia, Aug 02 2025

Formula

a(n) = sigma(8^n-1) = A000203(A024088(n)).
a(n) = A075708(3*n). - Max Alekseyev, Jan 09 2024

A366662 Sum of the divisors of 9^n-1.

Original entry on oeis.org

15, 186, 1680, 15876, 123690, 1541568, 8992680, 111757968, 967814400, 9366647892, 62424587520, 852903426816, 4766016364260, 55176998178240, 550081165885440, 4829754617483040, 31725040326819840, 471309320999516160, 2535353780263288800, 33995669076586206864
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(2)=186 because 9^2-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Links

Crossrefs

Cf. A024101, A000203, A366660, A366661, A366663.
Cf. A075708, A366576, A366603, A366613, A366622, A366634, A366653, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](9^n-1):
seq(a(n), n=1..30);
  • Mathematica
    DivisorSigma[1, 9^Range[30]-1]

Formula

a(n) = sigma(9^n-1) = A000203(A024101(n)).
a(n) = A366576(2*n) = A366576(n) * A366578(n) * (2^(4 + A007814(n)) - 1) / (2^(3 + A007814(n)) - 1) / 3. - Max Alekseyev, Jan 07 2024

A366603 Sum of the divisors of 4^n-1.

Original entry on oeis.org

4, 24, 104, 432, 1536, 8736, 22528, 111456, 473600, 1999872, 5909760, 38054016, 89522176, 462274560, 2015330304, 7304603328, 22907191296, 166290432000, 366506672128, 2220409884672, 7645340651520, 29833839544320, 95821839806976, 648494317126656
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(4)=432 because 4^4-1 has divisors {1, 3, 5, 15, 17, 51, 85, 255}.

Links

Crossrefs

Cf. A024036, A000203, A057957, A069061, A075708, A295501, A366602, A366604.
Cf. A075708, A366576, A366613, A366622, A366634, A366653, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](4^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1,4^Range[30]-1] (* Paolo Xausa, Oct 14 2023 *)

Formula

a(n) = sigma(4^n-1) = A000203(A024036(n)).
a(n) = A069061(n) * A075708(n). - Robert Israel, Nov 22 2023

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

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A024075, A000203, A057954, A059887, A074249, A218358, A366632, A366633, A366635.
Cf. A075708, A366576, A366603, A366613, A366622, A366653, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](7^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1, 7^Range[30]-1]

Formula

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

A366576 Sum of the divisors of 3^n-1.

Original entry on oeis.org

3, 15, 42, 186, 399, 1680, 3282, 15876, 31836, 123690, 277344, 1541568, 2391486, 8992680, 25483332, 111757968, 193819392, 967814400, 1744488660, 9366647892, 16912999320, 62424587520, 144219337920, 852903426816, 1397135488896, 4766016364260, 12477973754400
Offset: 1

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=186 because 3^4-1 has divisors {1, 2, 4, 5, 8, 10, 16, 20, 40, 80}.

Links

Crossrefs

Cf. A024023, A000203, A075708, A133801, A295500, A366575.
Cf. A075708, A366603, A366613, A366622, A366634, A366653, A366662, A102146, A366684, A366710.

Programs

  • Maple
    a:=n->numtheory[sigma](3^n-1):
seq(a(n), n=1..100);
  • Mathematica
    DivisorSigma[1,3^Range[30]-1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma(3^n-1) = A000203(A024023).

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

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024049, A001221, A057956, A059887, A074479, A143665, A218357, A295502, A366612, A366613.
Cf. A046800, A133801, A366604, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

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

Formula

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

A366617 Sum of the divisors of 5^n+1.

Original entry on oeis.org

3, 12, 42, 312, 942, 6264, 25284, 162000, 620460, 4961280, 16161768, 103442688, 367381884, 2441936064, 9859525284, 76963663296, 228970112844, 1526377433328, 6339280635408, 38199227335200, 144103649734968, 1285221510144000, 3894650946433800, 24349131482713344
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(3)=312 because 5^3+1 has divisors {1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 126}.

Links

Crossrefs

Cf. A000203, A034474, A057939, A074478, A366613, A366615, A366616, A366618.
Cf. A069061, A366578, A366607, A366629, A366638, A366657, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](5^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 5^Range[0, 30] + 1] (* Paolo Xausa, Jul 03 2024 *)

Formula

a(n) = sigma(5^n+1) = A000203(A034474(n)).
Showing 1-10 of 10 results.

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

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