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 11 results. Next

A366579 a(n) = phi(3^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 2, 4, 12, 40, 120, 288, 1092, 3072, 7776, 23600, 87120, 259200, 797160, 1847104, 5832000, 21523360, 63672480, 152845056, 580921200, 1700870400, 4368821184, 12550120000, 47071589412, 130459631616, 413939700000, 997562438080, 3012122557440, 11159367815680
Offset: 0

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Links

Crossrefs

Cf. A000010, A002592, A034472, A053285, A057935, A057941, A074476, A274909, A295500, A366577, A366578, A366580.

Programs

  • Mathematica
    EulerPhi[3^Range[0,30]+1] (* Paolo Xausa, Oct 15 2023 *)
  • PARI
    {a(n) = eulerphi(3^n+1)}

Formula

a(n) = phi(3^n+1) = A000010(A034472(n)).

A366577 Number of divisors of 3^n+1.

Original entry on oeis.org

2, 3, 4, 6, 4, 6, 8, 6, 8, 24, 12, 12, 8, 6, 16, 48, 4, 24, 16, 12, 8, 72, 16, 6, 64, 24, 16, 96, 16, 24, 48, 12, 4, 96, 16, 24, 16, 24, 16, 192, 32, 12, 128, 6, 32, 768, 16, 24, 16, 24, 128, 384, 16, 12, 32, 96, 64, 192, 16, 12, 128, 12, 32, 4608, 4, 24, 64
Offset: 0

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=4 because 3^4+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A000005, A002592, A034472, A046798, A057935, A057941, A074476, A274909, A366575, A366578, A366579, A366580

Programs

  • Maple
    a:=n->numtheory[tau](3^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0,3^Range[0,100]+1] (* Paolo Xausa, Oct 15 2023 *)
  • PARI
    a(n) = numdiv(3^n+1); \\ Michel Marcus, Oct 14 2023

Formula

a(n) = sigma0(3^n+1) = A000005(A034472(n)).

A366578 Sum of the divisors of 3^n+1.

Original entry on oeis.org

3, 7, 18, 56, 126, 434, 1332, 3836, 10476, 42560, 109926, 315112, 816732, 2790074, 8906760, 30220288, 64570086, 229156928, 706911048, 2034690952, 5357742012, 21838961760, 56496274632, 164750562956, 456919958880, 1517043139136, 4661686010664, 16489453890560
Offset: 0

Views

Author

Sean A. Irvine, Oct 13 2023

Keywords

Examples

			a(4)=126 because 3^4+1 has divisors {1, 2, 41, 82}.

Links

Crossrefs

Cf. A000203, A002592, A024023, A057935, A057941, A074476, A075708, A274909, A366576, A366577, A366579, A366580

Programs

  • Maple
    a:=n->numtheory[sigma](3^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[1,3^Range[0,30]+1] (* Paolo Xausa, Oct 15 2023 *)

Formula

a(n) = sigma(3^n+1) = A000203(A034472(n)).

A366660 Number of distinct prime divisors of 9^n - 1.

Original entry on oeis.org

1, 2, 3, 3, 3, 5, 3, 5, 6, 5, 5, 7, 3, 6, 8, 6, 6, 9, 5, 7, 8, 8, 4, 12, 7, 6, 11, 9, 7, 12, 6, 7, 10, 9, 8, 12, 6, 8, 12, 11, 6, 14, 4, 12, 16, 7, 8, 15, 10, 12, 13, 9, 6, 15, 11, 14, 13, 10, 5, 18, 5, 10, 16, 8, 9, 15, 6, 13, 13, 15, 7, 19, 7, 10, 19, 13, 11
Offset: 1

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A024101, A001221, A057952, A366661, A366662, A366663.
Cf. A046800, A133801, A366604, A366611, A366620, A366632, A366651, A102347, A366681, A366707.

Programs

  • PARI
    for(n = 1, 100, print1(omega(9^n - 1), ", "))

Formula

a(n) = omega(9^n-1) = A001221(A024101(n)).
a(n) = A133801(2*n) = A133801(n) + A366580(n) - 1. - 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)).

A366636 Number of distinct prime divisors of 7^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A034491, A001221, A057937, A227575, A366632, A366637, A366638, A366639.
Cf. A046799, A366580, A366605, A366615, A366627, A366655, A366664, A119704, A366686, A366712.

Programs

  • Mathematica
    PrimeNu[7^Range[0,84] + 1] (* Paul F. Marrero Romero, Nov 11 2023 *)
  • PARI
    for(n = 0, 100, print1(omega(7^n + 1), ", "))

Formula

a(n) = omega(7^n+1) = A001221(A034491(n)).

A366664 Number of distinct prime divisors of 9^n + 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Links

Crossrefs

Cf. A062396, A001221, A057935, A366660, A366665, A366666, A366667.
Cf. A046799, A366580, A366605, A366615, A366627, A366636, A366655, A119704, A366686, A366712.

Programs

  • Mathematica
    PrimeNu[9^Range[0,90]+1] (* Harvey P. Dale, Jul 04 2024 *)
  • PARI
    for(n = 0, 100, print1(omega(9^n + 1), ", "))

Formula

a(n) = omega(9^n+1) = A001221(A062396(n)).
a(n) = A366580(2*n). - Max Alekseyev, Jan 08 2024
Showing 1-10 of 11 results. Next

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

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