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 1-3 of 3 results.

A366899 Number of prime factors of n*2^n - 1, counted with multiplicity.

Original entry on oeis.org

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

Views

Author

Tyler Busby, Oct 26 2023

Keywords

Comments

The numbers n*2^n-1 are called Woodall (or Riesel) numbers.

Links

Crossrefs

Cf. A001222, A003261, A085723, A366898 (divisors), A367006 (without multiplicity).

Programs

  • Mathematica
    Table[PrimeOmega[n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 09 2023 *)
  • PARI
    a(n) = bigomega(n*2^n - 1); \\ Michel Marcus, Dec 09 2023

Formula

a(n) = bigomega(n*2^n - 1) = A001222(A003261(n)).

A367006 Number of distinct prime factors of n*2^n - 1.

Original entry on oeis.org

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

Views

Author

Sean A. Irvine, Oct 31 2023

Keywords

Comments

The numbers n*2^n-1 are called Woodall (or Riesel) numbers.

Links

Crossrefs

Cf. A003261, A001221, A366898, A366899.

Programs

  • Mathematica
    Table[PrimeNu[n*2^n - 1], {n, 1, 100}] (* Amiram Eldar, Dec 11 2023 *)
  • PARI
    a(n) = omega(n*2^n - 1); \\ Amiram Eldar, Dec 11 2023

Formula

a(n) = omega(n*2^n - 1) = A001221(A003261(n)).

A367009 Number of divisors of n*2^n + 1.

Original entry on oeis.org

1, 2, 3, 3, 4, 4, 8, 8, 4, 4, 12, 4, 8, 6, 8, 8, 4, 12, 16, 16, 16, 4, 16, 16, 16, 16, 24, 16, 6, 8, 48, 48, 8, 4, 32, 4, 12, 8, 12, 8, 8, 16, 16, 32, 16, 16, 32, 32, 16, 10, 64, 8, 64, 8, 32, 16, 12, 32, 32, 16, 16, 128, 8, 8, 96, 32, 256, 24, 16, 32, 32, 48
Offset: 0

Views

Author

Sean A. Irvine, Oct 31 2023

Keywords

Comments

The numbers n*2^n+1 are called Cullen numbers.

Links

Crossrefs

Cf. A002064, A000005, A366898, A367007, A367008.

Programs

  • Mathematica
    Table[DivisorSigma[0, n*2^n + 1], {n, 0, 100}] (* Amiram Eldar, Jan 06 2024 *)
  • PARI
    a(n) = numdiv(n*2^n + 1); \\ Amiram Eldar, Jan 06 2024

Formula

a(n) = sigma0(n*2^n + 1) = A000005(A002064(n)).
Showing 1-3 of 3 results.

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

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