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 22 results. Next

A069061 Sum of divisors of 2^n+1.

Original entry on oeis.org

4, 6, 13, 18, 48, 84, 176, 258, 800, 1302, 2736, 4356, 10928, 20520, 51792, 65538, 174768, 351120, 699056, 1110276, 3100240, 5048232, 11184816, 17041416, 49012992, 82623888, 211053040, 284225796, 727960800, 1494039792, 2863311536, 4301668356, 12611914848, 20788904016
Offset: 1

Views

Author

Benoit Cloitre, Apr 04 2002

Keywords

Links

Crossrefs

Cf. A000051, A000203, A002185, A002587, A002589, A046798, A046799, A053285, A054992, A057957, A059886, A085029, A086257, A112092, A250291, A274906, A295501.
Row sums of A374237.

Programs

  • Mathematica
    DivisorSigma[1, 2^Range[50] + 1] (* Paolo Xausa, Jul 05 2024 *)
  • PARI
    a(n) = sigma(2^n+1); \\ Michel Marcus, Nov 24 2013

Formula

a(n) = sigma(2^n+1).
a(n) = A000203(A000051(n)). - Michel Marcus, Nov 24 2013

Extensions

More terms from Amiram Eldar, Oct 04 2019

A366712 Number of distinct prime divisors of 12^n + 1.

Original entry on oeis.org

1, 1, 2, 3, 2, 2, 3, 3, 3, 5, 3, 2, 4, 4, 4, 7, 2, 3, 5, 4, 6, 8, 6, 4, 6, 6, 5, 10, 3, 3, 5, 3, 2, 9, 4, 5, 7, 4, 5, 10, 4, 5, 6, 5, 4, 12, 3, 5, 5, 5, 8, 9, 5, 5, 10, 7, 9, 10, 7, 6, 10, 5, 6, 14, 5, 8, 11, 4, 5, 12, 9, 3, 10, 5, 8, 17, 5, 6, 9, 4, 6, 15, 3
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A001221, A046799, A119704, A366713, A366714, A366707, A366686.

Programs

  • PARI
    for(n = 0, 100, print1(omega(12^n + 1), ", "))

Formula

a(n) = omega(12^n+1) = A001221(A178248(n)).

A053285 Totient of 2^n+1.

Original entry on oeis.org

1, 2, 4, 6, 16, 20, 48, 84, 256, 324, 800, 1364, 3840, 5460, 12544, 19800, 65536, 87380, 186624, 349524, 986880, 1365336, 3345408, 5592404, 16515072, 20250000, 52306176, 84768120, 252645120, 351847488, 760320000, 1431655764, 4288266240, 5632621632, 13628740608
Offset: 0

Views

Author

Labos Elemer, Mar 03 2000

Keywords

Examples

			It is a power of 2 iff n is a Fermat prime.

Links

Crossrefs

Cf. A000010, A000225, A002587, A000051, A046798, A046799, A049479, A051953, A054992.

Programs

Formula

a(n) = A000010(A000051(n)).

Extensions

a(0)=1 prepended by Alois P. Heinz, Aug 12 2015

A366580 Number of distinct prime divisors of 3^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Links

Crossrefs

Cf. A001221, A002592, A034472, A046799, A057935, A057941, A074476, A133801, A274909, A366577, A366578, A366579.

Programs

  • Mathematica
    PrimeNu[3^Range[0,100]+1] (* Paolo Xausa, Oct 14 2023 *)
  • PARI
    for(n = 0, 100, print1(omega(3^n + 1), ", "))

Formula

a(n) = omega(3^n+1) = A001221(A034472(n)).

A366686 Number of distinct prime divisors of 11^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001221, A366681, A102347, A366687, A366688, A366689, A366690.
Cf. A046799, A119704, A366712.

Programs

  • PARI
    for(n = 0, 100, print1(omega(11^n + 1), ", "))

Formula

a(n) = omega(11^n+1) = A001221(A034524(n)).

A366604 Number of distinct prime divisors of 4^n - 1.

Original entry on oeis.org

1, 2, 2, 3, 3, 4, 3, 4, 4, 5, 4, 6, 3, 6, 6, 5, 3, 8, 3, 7, 6, 7, 4, 9, 7, 7, 6, 8, 6, 11, 3, 7, 8, 7, 9, 12, 5, 7, 7, 9, 5, 12, 5, 10, 11, 9, 6, 12, 5, 12, 10, 10, 6, 12, 11, 11, 8, 9, 6, 15, 3, 8, 11, 9, 9, 14, 5, 10, 8, 15, 6, 17, 6, 10, 13, 11, 10, 16, 5
Offset: 1

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A024036, A001221, A057957, A133801, A366602, A366603.
Cf. A046800, A133801, A366611, A366620, A366632, A366651, A366660, A102347, A366681, A366707.

Programs

  • Mathematica
    PrimeNu[4^Range[100]-1] (* Paolo Xausa, Oct 14 2023 *)
  • PARI
    for(n = 1, 100, print1(omega(4^n - 1), ", "))
  • Python
    from sympy import primenu
def A366604(n): return primenu((1<<(n<<1))-1) # Chai Wah Wu, Oct 15 2023

Formula

a(n) = omega(4^n-1) = A001221(A024036(n)).
a(n) = A046800(2*n) = A046799(n) + A046800(n). - Max Alekseyev, Jan 07 2024

A366605 Number of distinct prime divisors of 4^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A001221, A052539, A057940, A274903, A366604, A366606, A366607, A366608, A366609.
Cf. A046799, A366580, A366615, A366627, A366636, A366655, A366664, A119704, A366686, A366712.

Programs

  • Mathematica
    PrimeNu[4^Range[0,100]+1] (* Paolo Xausa, Oct 14 2023 *)
  • PARI
    for(n = 0, 100, print1(omega(4^n + 1), ", "))
  • Python
    from sympy import primenu
def A366605(n): return primenu((1<<(n<<1))+1) # Chai Wah Wu, Oct 14 2023

Formula

a(n) = omega(4^n+1) = A001221(A052539(n)).
a(n) = A046799(2*n). - Max Alekseyev, Jan 08 2024

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

A366615 Number of distinct prime divisors of 5^n + 1.

Original entry on oeis.org

1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 3, 6, 3, 4, 5, 5, 4, 8, 4, 4, 4, 5, 4, 7, 3, 4, 7, 5, 4, 8, 6, 7, 6, 5, 4, 7, 5, 6, 6, 6, 3, 8, 3, 5, 5, 7, 7, 9, 5, 5, 6, 7, 7, 8, 3, 6, 6, 6, 4, 13, 4, 8, 7, 3, 7, 8, 7, 5, 6, 5, 5, 12, 5, 9, 9, 6, 6, 10, 6, 5, 7, 9
Offset: 0

Views

Author

Sean A. Irvine, Oct 14 2023

Keywords

Links

Crossrefs

Cf. A001221, A034474, A057939, A074478, A366611, A366616, A366617, A366618.
Cf. A046799, A366580, A366605, A366627, A366636, A366655, A366664, A119704, A366686, A366712.

Programs

  • Mathematica
    Table[PrimeNu[5^n+1],{n,0,90}] (* Harvey P. Dale, Apr 06 2025 *)
  • PARI
    for(n = 0, 100, print1(omega(5^n + 1), ", "))

Formula

a(n) = omega(5^n+1) = A001221(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)).
Showing 1-10 of 22 results. Next

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