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 1-7 of 7 results.

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)).

A366714 Number of divisors of 12^n+1.

Original entry on oeis.org

2, 2, 4, 8, 4, 4, 8, 8, 8, 32, 12, 4, 16, 24, 16, 128, 4, 8, 32, 16, 64, 384, 64, 16, 64, 64, 32, 1024, 8, 8, 48, 8, 4, 512, 16, 32, 128, 16, 32, 1536, 16, 32, 64, 32, 16, 4096, 8, 32, 32, 32, 512, 512, 32, 32, 1024, 128, 512, 1536, 192, 64, 1024, 32, 64
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Examples

			a(4)=4 because 12^4+1 has divisors {1, 89, 233, 20737}.

Links

Crossrefs

Cf. A178248, A000005, A046798, A344897, A366709, A366712, A366713, A366715, A366716, A366719, A366720, A366688.

Programs

  • Maple
    a:=n->numtheory[tau](12^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 12^Range[0, 70] + 1] (* Paolo Xausa, Apr 20 2025 *)
  • PARI
    a(n) = numdiv(12^n+1);

Formula

a(n) = sigma0(12^n+1) = A000005(A178248(n)).

A366716 a(n) = phi(12^n+1), where phi is Euler's totient function (A000010).

Original entry on oeis.org

1, 12, 112, 1296, 20416, 229680, 2306304, 32916240, 400515072, 3863116800, 47825825600, 685853880624, 8732596764672, 97509650382144, 990242755633152, 11148606564480000, 184883057981234176, 2047145911595946000, 20281543142263603200, 294779525244632305920
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A000010, A366711, A366712, A366713, A366714, A366715, A366719, A366720, A366690.

Programs

  • Mathematica
    EulerPhi[12^Range[0,19] + 1] (* Paul F. Marrero Romero, Oct 27 2023 *)
  • PARI
    {a(n) = eulerphi(12^n+1)}

Formula

a(n) = A000010(A178248(n)). - Paul F. Marrero Romero, Oct 27 2023

A366715 Sum of the divisors of 12^n+1.

Original entry on oeis.org

3, 14, 180, 2240, 21060, 267988, 3706920, 38773952, 459970056, 6692483840, 79425033660, 800162860756, 9101898907920, 117326869641600, 1596198064568400, 20655000929239040, 184885459808838660, 2390210102271311936, 33504016991491136160, 344201347103878781440
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Examples

			a(4)=21060 because 12^4+1 has divisors {1, 89, 233, 20737}.

Links

Crossrefs

Cf. A178248, A000203, A366710, A366712, A366713, A366714, A366716, A366719, A366720, A366689.

Programs

  • Maple
    a:=n->numtheory[sigma](12^n+1):
seq(a(n), n=0..100);

Formula

a(n) = sigma(12^n+1) = A000203(A178248(n)).

A366719 Smallest prime dividing 12^n + 1.

Original entry on oeis.org

2, 13, 5, 7, 89, 13, 5, 13, 17, 7, 5, 13, 89, 13, 5, 7, 153953, 13, 5, 13, 41, 7, 5, 13, 17, 13, 5, 7, 89, 13, 5, 13, 769, 7, 5, 13, 89, 13, 5, 7, 17, 13, 5, 13, 89, 7, 5, 13, 7489, 13, 5, 7, 89, 13, 5, 13, 17, 7, 5, 13, 41, 13, 5, 7, 36097, 13, 5, 13, 89, 7
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A002586, A038371, A178248, A366712, A366713, A366714, A366715, A366716, A366717, A366720.

Programs

Formula

a(n) = A020639(A178248(n)). - Paul F. Marrero Romero, Oct 25 2023

A366687 Number of prime factors of 11^n + 1 (counted with multiplicity).

Original entry on oeis.org

1, 3, 2, 5, 2, 4, 4, 4, 3, 7, 3, 7, 4, 6, 5, 8, 3, 6, 5, 7, 4, 7, 4, 7, 7, 6, 3, 10, 6, 6, 6, 7, 4, 13, 6, 11, 7, 5, 4, 11, 5, 6, 9, 5, 6, 13, 6, 7, 5, 8, 6, 11, 3, 7, 9, 13, 7, 12, 6, 7, 8, 6, 4, 13, 3, 10, 8, 9, 7, 14, 8, 6, 10, 8, 8, 13, 6, 12, 12, 7, 10
Offset: 0

Views

Author

Sean A. Irvine, Oct 16 2023

Keywords

Links

Crossrefs

Cf. A034524, A001222, A057934, A062308, A366686, A366688, A366689, A366690.
Cf. A054992, A057941, A057940, A057939, A057938, A057937, A057936, A057935, A057934, A366713.

Programs

  • Mathematica
    PrimeOmega[11^Range[70]+1]
  • PARI
    a(n)=bigomega(11^n+1)

Formula

a(n) = bigomega(11^n+1) = A001222(A034524(n)).

A366720 Largest prime factor of 12^n+1.

Original entry on oeis.org

2, 13, 29, 19, 233, 19141, 20593, 13063, 260753, 1801, 85403261, 57154490053, 2227777, 222379, 13156924369, 35671, 1200913648289, 66900193189411, 122138321401, 905265296671, 67657441, 1885339, 68368660537, 49489630860836437, 592734049, 438472201
Offset: 0

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A006530, A002587, A074476, A274903, A074478, A274904, A227575, A274905, A002592, A003021, A062308, A002590, A366712, A366713, A366714, A366715, A366716, A366717, A366718, A366719, A324941.

Programs

  • Mathematica
    Table[FactorInteger[12^n + 1][[-1, 1]], {n, 0, 20}]

Formula

a(n) = A006530(A178248(n)). - Paul F. Marrero Romero, Dec 07 2023
Showing 1-7 of 7 results.

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