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.

Previous Showing 11-14 of 14 results.

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)).

A366637 Number of divisors of 7^n+1.

Original entry on oeis.org

2, 4, 6, 8, 4, 16, 24, 16, 8, 16, 32, 16, 32, 16, 12, 64, 8, 8, 48, 16, 16, 128, 48, 8, 16, 32, 24, 32, 64, 8, 512, 32, 16, 128, 48, 1024, 256, 16, 12, 256, 64, 64, 96, 512, 32, 2048, 96, 8, 64, 2048, 640, 128, 32, 64, 384, 3072, 256, 256, 96, 64, 512, 8, 48
Offset: 0

Views

Author

Sean A. Irvine, Oct 15 2023

Keywords

Examples

			a(4)=4 because 7^4+1 has divisors {1, 2, 1201, 2402}.

Links

Crossrefs

Cf. A034491, A000005, A057937, A227575, A366633, A366636, A366638, A366639.
Cf. A046798, A366577, A366606, A366616, A366628, A366656, A366665, A344897, A366688, A366714.

Programs

  • Maple
    a:=n->numtheory[tau](7^n+1):
seq(a(n), n=0..100);
  • Mathematica
    DivisorSigma[0, 7^Range[0, 62] + 1] (* Paul F. Marrero Romero, Oct 16 2023 *)
  • PARI
    a(n) = numdiv(7^n+1);

Formula

a(n) = sigma0(7^n+1) = A000005(A034491(n)).

A366713 Number of prime factors of 12^n + 1 (counted with multiplicity).

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 17 2023

Keywords

Links

Crossrefs

Cf. A178248, A001222, A054992, A057934, A057935, A057936, A057937, A057938, A057939, A057940, A057941, A366712, A366714, A366715, A366716, A366719, A366720, A366708, A366687.

Programs

  • Mathematica
    PrimeOmega[12^Range[70]+1]
  • PARI
    a(n)=bigomega(12^n+1)

Formula

a(n) = bigomega(12^n+1) = A001222(A178248(n)).

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)).
Previous Showing 11-14 of 14 results.

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