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.

A345047 a(n) = A003958(n) / A345046(n), where A003958(n) is multiplicative with a(p^e) = (p-1)^e, and A345046(n) gives the least common multiple of the same factors.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 4, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 4, 1, 2, 1, 1, 4, 6, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 4
Offset: 1

Views

Author

Antti Karttunen, Jun 07 2021

Keywords

Crossrefs

Cf. also A345045, A353784.

Programs

  • PARI
    A345047(n) = { my(f=factor(n)~, g=vector(#f, i, (f[1, i]-1)^f[2, i])); factorback(g)/lcm(g); };

Formula

a(n) = A003958(n) / A345046(n).

A353783 a(n) = LCM_{p^e||n} sigma(p^e), where n = Product_{p^e||n}, with each p^e the maximal power of prime p that divides n.

Original entry on oeis.org

1, 3, 4, 7, 6, 12, 8, 15, 13, 6, 12, 28, 14, 24, 12, 31, 18, 39, 20, 42, 8, 12, 24, 60, 31, 42, 40, 56, 30, 12, 32, 63, 12, 18, 24, 91, 38, 60, 28, 30, 42, 24, 44, 84, 78, 24, 48, 124, 57, 93, 36, 14, 54, 120, 12, 120, 20, 30, 60, 84, 62, 96, 104, 127, 42, 12, 68, 126, 24, 24, 72, 195, 74, 114, 124, 140, 24, 84, 80
Offset: 1

Views

Author

Antti Karttunen, May 08 2022

Keywords

Crossrefs

Cf. also A345044, A345046.
Cf. A336547 (positions where equal to sigma).

Programs

  • Mathematica
    Array[LCM @@ DivisorSigma[1, Power @@@ FactorInteger[#]] &, 79] (* Michael De Vlieger, May 08 2022 *)
  • PARI
    A353783(n) = { my(f=factor(n)~); lcm(vector(#f, i, sigma(f[1, i]^f[2, i]))); };

Formula

a(n) = A000203(n) / A353784(n).
a(n) = A353785(n) * A080398(n).
For all n >= 1, A087207(a(n)) = A351560(n).

A345044 If n = Product p(k)^e(k) then a(n) = LCM (p(k)^e(k) - 1).

Original entry on oeis.org

1, 1, 2, 3, 4, 2, 6, 7, 8, 4, 10, 6, 12, 6, 4, 15, 16, 8, 18, 12, 6, 10, 22, 14, 24, 12, 26, 6, 28, 4, 30, 31, 10, 16, 12, 24, 36, 18, 12, 28, 40, 6, 42, 30, 8, 22, 46, 30, 48, 24, 16, 12, 52, 26, 20, 42, 18, 28, 58, 12, 60, 30, 24, 63, 12, 10, 66, 48, 22, 12, 70, 56, 72, 36, 24, 18, 30, 12, 78, 60, 80, 40, 82, 6, 16, 42
Offset: 1

Views

Author

Antti Karttunen, Jun 07 2021

Keywords

Crossrefs

Programs

  • PARI
    A345044(n) = { my(f=factor(n)~); lcm(vector(#f, i, (f[1, i]^f[2, i])-1)); };

Formula

a(n) = A047994(n) / A345045(n).
Showing 1-3 of 3 results.