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 1-8 of 8 results.

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

A366629 Sum of the divisors of 6^n+1.

Original entry on oeis.org

3, 8, 38, 256, 1298, 9792, 52136, 338580, 1778436, 11889152, 62367272, 414625216, 2178461956, 15224775552, 80673299432, 611106029568, 2830769440776, 19344856702976, 115255634181184, 696800841097536, 3748220725527432, 27388329197137920, 135183433256806480
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Examples

			a(3)=256 because 6^3+1 has divisors {1, 7, 31, 217}.

Links

Crossrefs

Cf. A062394, A000203, A057938, A366622, A366617, A366627, A366628, A366630, A366670.
Cf. A069061, A366578, A366607, A366638, A366657, A366666, A366668, A366689, A366715.

Programs

  • Maple
    a:=n->numtheory[sigma](6^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1, 6^Range[0, 30] + 1] (* Paolo Xausa, Jul 03 2024 *)

Formula

a(n) = sigma(6^n+1) = A000203(A062394(n)).

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)).

A366655 Number of distinct prime divisors of 8^n + 1.

Original entry on oeis.org

1, 1, 2, 2, 2, 3, 4, 3, 3, 3, 5, 4, 4, 3, 6, 5, 3, 5, 6, 4, 4, 5, 6, 4, 5, 6, 9, 6, 5, 4, 10, 4, 3, 7, 9, 10, 6, 6, 8, 5, 6, 6, 10, 5, 7, 9, 8, 6, 7, 6, 12, 9, 5, 5, 10, 10, 8, 6, 8, 7, 8, 3, 9, 10, 4, 10, 12, 7, 8, 6, 14, 7, 8, 5, 10, 10, 8, 11, 16, 5, 7, 10
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A062395, A001221, A057936, A274905, A366651, A366632, A366656, A366657, A366658, A366671.
Cf. A046799, A366580, A366605, A366615, A366627, A366636, A366664, A119704, A366686, A366712.

Programs

  • PARI
    for(n = 0, 100, print1(omega(8^n + 1), ", "))

Formula

a(n) = omega(8^n+1) = A001221(A062395(n)).
a(n) = A046799(3*n). - Max Alekseyev, Jan 09 2024

A366658 a(n) = phi(8^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 6, 48, 324, 3840, 19800, 186624, 1365336, 16515072, 84768120, 760320000, 5632621632, 64258375680, 366369658200, 3105655160832, 20140520400000, 280012271910912, 1495522910085120, 12824556668190720, 95907982079387520, 1080582572777472000, 5688765822212629632
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A062395, A000010, A057936, A274905, A366654, A366655, A366656, A366657, A366671.
Cf. A053285, A366579, A366608, A366618, A366630, A366639, A366667, A366669, A366690, A366716.

Programs

  • Mathematica
    EulerPhi[8^Range[0, 21] + 1] (* Paul F. Marrero Romero, Oct 17 2023 *)
  • PARI
    {a(n) = eulerphi(8^n+1)}
  • Python
    from sympy import totient
def A366658(n): return totient((1<<3*n)+1) # Chai Wah Wu, Oct 15 2023

Formula

a(n) = A000010(A062395(n)). - Paul F. Marrero Romero, Nov 06 2023
a(n) = A053285(3*n). - Max Alekseyev, Jan 09 2024

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)).

A366656 Number of divisors of 8^n+1.

Original entry on oeis.org

2, 3, 4, 8, 4, 12, 16, 12, 8, 20, 48, 24, 16, 12, 64, 64, 8, 48, 64, 24, 16, 64, 64, 24, 32, 96, 768, 192, 32, 24, 1536, 24, 8, 256, 512, 1536, 64, 96, 256, 64, 64, 96, 1024, 48, 128, 1280, 256, 96, 128, 96, 8192, 1024, 32, 48, 1024, 2304, 256, 192, 256, 192
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

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

Links

Crossrefs

Cf. A062395, A000005, A057936, A274905, A366653, A366638, A366655, A366657, A366658.
Cf. A046798, A366577, A366606, A366616, A366628, A366637, A366665, A344897, A366688, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](8^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 8^Range[0,59] + 1] (* Paul F. Marrero Romero, Nov 12 2023 *)
  • PARI
    a(n) = numdiv(8^n+1);

Formula

a(n) = sigma0(8^n+1) = A000005(A062395(n)).
a(n) = A046798(3*n). - Max Alekseyev, Jan 09 2024
Showing 1-8 of 8 results.

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

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