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 1-9 of 9 results.

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)).

A366666 Sum of the divisors of 9^n+1.

Original entry on oeis.org

3, 18, 126, 1332, 10476, 109926, 816732, 8906760, 64570086, 706911048, 5357742012, 56496274632, 456919958880, 4661686010664, 35152280388792, 388532214509688, 2779530283277766, 30018958465575240, 230668806145962744, 2431533550553980488, 19410628990783168944
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(2)=126 because 9^2+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A062396, A000203, A057935, A366662, A366664, A366665, A366667.
Cf. A069061, A366578, A366607, A366617, A366629, A366638, A366657, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](9^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 9^Range[0,20] + 1] (* Paul F. Marrero Romero, Nov 14 2023 *)

Formula

a(n) = sigma(9^n+1) = A000203(A062396(n)).
a(n) = A366578(2*n). - Max Alekseyev, Jan 08 2024

A366607 Sum of the divisors of 4^n+1.

Original entry on oeis.org

3, 6, 18, 84, 258, 1302, 4356, 20520, 65538, 351120, 1110276, 5048232, 17041416, 82623888, 284225796, 1494039792, 4301668356, 20788904016, 73234343952, 332019460560, 1103789883396, 5936210280000, 18679788287496, 84884999116320, 282937726148616
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(3)=84 because 4^3+1 has divisors {1, 5, 13, 65}.

Links

Crossrefs

Cf. A000203, A052539, A057940, A274903, A366603, A366605, A366606, A366608, A366609.
Cf. A069061, A366578, A366617, A366629, A366638, A366657, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](4^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1,4^Range[0,30]+1] (* Paolo Xausa, Oct 14 2023 *)
  • Python
    from sympy import divisor_sigma
def A366607(n): return divisor_sigma((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

Formula

a(n) = sigma(4^n+1) = A000203(A052539(n)).
a(n) = A069061(2*n). - Max Alekseyev, Jan 08 2024

A366630 a(n) = phi(6^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 6, 36, 180, 1296, 6000, 41472, 230496, 1580800, 8359200, 58579200, 310968900, 2175102720, 10971642240, 76065091200, 351048600000, 2811459796992, 14508487949472, 88870766837760, 522016066337712, 3564233663616000, 17479898551382400, 128060205344805888
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A062394, A000010, A366623, A366618, A366627, A366628, A366629, A366670.
Cf. A053285, A366579, A366608, A366639, A366658, A366667, A366669, A366690, A366716.

Programs

  • Mathematica
    EulerPhi[6^Range[0, 22] + 1] (* Paul F. Marrero Romero, Oct 17 2023 *)
  • PARI
    {a(n) = eulerphi(6^n+1)}

Formula

a(n) = A000010(A062394(n)). - Paul F. Marrero Romero, Oct 17 2023

A366638 Sum of the divisors of 7^n+1.

Original entry on oeis.org

3, 15, 93, 660, 3606, 34560, 236964, 1559520, 9155916, 77423280, 530807472, 3868683120, 21224771760, 185094572580, 1261494915594, 9988783073280, 49990612274316, 436182213726030, 3279858902194056, 21372989348391720, 122709716651985624, 1082323574100172800
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(4)=3606 because 7^4+1 has divisors {1, 2, 1201, 2402}.

Links

Crossrefs

Cf. A034491, A000203, A057937, A227575, A366634, A366636, A366637, A366639.
Cf. A069061, A366578, A366607, A366617, A366629, A366657, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](7^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 7^Range[0, 21] + 1] (* Paul F. Marrero Romero, Oct 16 2023 *)

Formula

a(n) = sigma(7^n+1) = A000203(A034491(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)).

A366627 Number of distinct prime divisors of 6^n + 1.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 3, 3, 2, 3, 3, 2, 2, 4, 3, 5, 3, 3, 6, 3, 3, 5, 4, 3, 4, 4, 4, 5, 5, 4, 9, 2, 3, 6, 3, 10, 5, 4, 3, 9, 5, 4, 7, 2, 3, 7, 5, 2, 7, 5, 6, 8, 4, 5, 10, 7, 6, 7, 3, 2, 6, 3, 2, 9, 3, 8, 11, 5, 5, 6, 7, 4, 5, 6, 4, 10, 5, 5, 10, 6, 6, 8, 4, 5, 8
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A062394, A001221, A057938, A366620, A366628, A366629, A366630.
Cf. A046799, A366580, A366605, A366615, A366636, A366655, A366664, A119704, A366686, A366712.

Programs

  • Mathematica
    PrimeNu[6^Range[0,84] + 1] (* Paul F. Marrero Romero, Nov 11 2023 *)
  • PARI
    for(n = 0, 100, print1(omega(6^n + 1), ", "))

Formula

a(n) = omega(6^n+1) = A001221(A062394(n)).

A366628 Number of divisors of 6^n+1.

Original entry on oeis.org

2, 2, 2, 4, 2, 8, 8, 12, 4, 8, 8, 4, 4, 16, 8, 32, 8, 8, 64, 8, 8, 48, 16, 8, 16, 16, 16, 32, 32, 16, 512, 4, 8, 64, 8, 1536, 32, 16, 8, 512, 32, 16, 128, 4, 8, 128, 32, 4, 128, 64, 64, 256, 16, 32, 1024, 192, 64, 128, 8, 4, 64, 8, 4, 768, 8, 256, 2048, 32, 32
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(3)=4 because 6^3+1 has divisors {1, 7, 31, 217}.

Links

Crossrefs

Cf. A062394, A000005, A057938, A366621, A366627, A366629, A366630, A366670.
Cf. A046798, A366577, A366606, A366616, A366637, A366656, A366665, A344897, A366688, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](6^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 6^Range[0, 70] + 1] (* Paolo Xausa, Apr 19 2025 *)
  • PARI
    a(n) = numdiv(6^n+1);

Formula

a(n) = sigma0(6^n+1) = A000005(A062394(n)).

A366657 Sum of the divisors of 8^n+1.

Original entry on oeis.org

3, 13, 84, 800, 4356, 51792, 351120, 3100240, 17041416, 211053040, 1494039792, 12611914848, 73234343952, 794382536272, 5936210280000, 60037292774400, 282937726148616, 3264911394064320, 24128875076496960, 208532141890460960, 1225825603154905104
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(4)=4356 because 8^4+1 has divisors {1, 17, 241, 4097}.

Links

Crossrefs

Cf. A062395, A000203, A057936, A274905, A366653, A366655, A366656, A366658.
Cf. A069061, A366578, A366607, A366617, A366629, A366638, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](8^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 8^Range[0,20]+1] (* Paul F. Marrero Romero, Nov 19 2023 *)

Formula

a(n) = sigma(8^n+1) = A000203(A062395(n)).
a(n) = A069061(3*n). - Max Alekseyev, Jan 09 2024
Showing 1-9 of 9 results.

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