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 13 results. Next

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

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

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)).

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)).

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

A096855 a(n) = A062401(2^n + 1).

Original entry on oeis.org

2, 2, 2, 12, 6, 16, 24, 80, 84, 320, 360, 864, 1320, 5456, 5184, 15744, 19800, 52800, 69120, 349520, 370080, 1036800, 1425600, 3640896, 4741632, 13989888, 27091584, 76743040, 94656000, 166387200, 412473600, 1407389952, 1420488192, 3459760128, 6502788864, 14778408960
Offset: 0

Views

Author

Labos Elemer, Jul 19 2004

Keywords

Links

Crossrefs

Cf. A000010, A062401, A062402, A053287, A096853, A069061, A096854, A096855, A096856.

Programs

  • Mathematica
    Table[ EulerPhi[ DivisorSigma[1, 2^n+1]], {n, 0, 33}]

Formula

a(n) = A000010(A069061(n)). - Amiram Eldar, Jun 04 2024

Extensions

Edited and extended by Robert G. Wilson v, Jul 23 2004
Offset changed to 0, a(0) prepended and two more terms added by Amiram Eldar, Jun 04 2024

A374237 Irregular triangle read by rows where row n lists, in increasing order, the divisors of 2^n + 1.

Original entry on oeis.org

1, 2, 1, 3, 1, 5, 1, 3, 9, 1, 17, 1, 3, 11, 33, 1, 5, 13, 65, 1, 3, 43, 129, 1, 257, 1, 3, 9, 19, 27, 57, 171, 513, 1, 5, 25, 41, 205, 1025, 1, 3, 683, 2049, 1, 17, 241, 4097, 1, 3, 2731, 8193, 1, 5, 29, 113, 145, 565, 3277, 16385, 1, 3, 9, 11, 33, 99, 331, 993, 2979, 3641, 10923, 32769
Offset: 0

Views

Author

Paolo Xausa, Jul 02 2024

Keywords

Examples

			Triangle begins:
   [0]  1,   2;
   [1]  1,   3;
   [2]  1,   5;
   [3]  1,   3,  9;
   [4]  1,  17;
   [5]  1,   3, 11,  33;
   [6]  1,   5, 13,  65;
   [7]  1,   3, 43, 129;
   [8]  1, 257;
   [9]  1,   3,  9,  19,  27,   57, 171, 513;
  [10]  1,   5, 25,  41, 205, 1025;
  ...

Links

Crossrefs

Subsequence of A027750.
Cf. A000051, A002586 (2nd column), A046798 (row lengths), A069060 (row products), A069061 (row sums).
Cf. A361438 (analogous for 2^n - 1).

Programs

  • Maple
    T:= n-> sort([numtheory[divisors](2^n+1)[]])[]:
seq(T(n), n=0..15);  # Alois P. Heinz, Oct 20 2024
  • Mathematica
    Divisors[2^Range[0, 20] + 1]

A067718 Numbers k such that sigma(2^k+1) == 0 (mod k).

Original entry on oeis.org

1, 2, 6, 12, 24, 36, 42, 70, 126, 132, 144, 168, 210, 225, 252, 336, 344, 378, 385, 396, 462, 504, 528, 546, 560, 561, 576, 627, 630, 660, 672, 693, 714, 798, 896, 924, 930, 945, 960, 1001, 1008, 1012, 1032, 1050, 1116
Offset: 1

Views

Author

Benoit Cloitre, Feb 05 2002

Keywords

Comments

1155 is also a term. - Husnain Raza, Oct 23 2024

Links

Crossrefs

Cf. A000051, A000203, A069061.

Programs

  • Mathematica
    Select[Range[150], Divisible[DivisorSigma[1, 2^# + 1], #] &] (* Amiram Eldar, Nov 28 2020 *)
  • PARI
    isok(n)=sigma(2^n+1)%n==0 \\ Klaus Brockhaus, Apr 13 2005

Extensions

a(13)-a(15) from Klaus Brockhaus, Apr 13 2005
a(16)-a(21) from Lars Blomberg, Jul 28 2017
a(22)-a(44) from Amiram Eldar, Nov 28 2020
a(45) from Husnain Raza, Sep 18 2024
Showing 1-10 of 13 results. Next

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

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