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.

A351436 a(n) = n - A351168(n).

Original entry on oeis.org

0, 1, 1, 3, 1, 2, 1, 7, 5, 2, 1, 4, 1, 2, 3, 15, 1, 10, 1, 4, 3, 2, 1, 8, 9, 2, 19, 4, 1, 6, 1, 31, 3, 2, 5, 20, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 13, 18, 3, 4, 1, 38, 5, 8, 3, 2, 1, 12, 1, 2, 9, 63, 5, 6, 1, 4, 3, 10, 1, 40, 1, 2, 27, 4, 7, 6, 1, 16, 65, 2
Offset: 1

Views

Author

Ben Polson, Feb 11 2022

Keywords

Crossrefs

Cf. A351168, A006530 (largest prime factor), A071178 (exponent).

Programs

  • Mathematica
    a[n_] := n - Module[{f = FactorInteger[n]}, n*(1 - 1/f[[-1, 1]])^f[[-1, 2]]]; a[1] = 0; Table[a[n], {n, 2, 83}] (* Robert P. P. McKone, Feb 11 2022, from Amiram Eldar in A351168 *)

Formula

a(n) = n * (1 - ((A006530(n) - 1)/A006530(n))^A071178).

A351419 If n = p_1^e_1 * ... * p_k^e_k, where p_1 < ... < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k - 1)^(e_k + 1); a(1) = 1.

Original entry on oeis.org

1, 1, 4, 1, 16, 8, 36, 1, 8, 32, 100, 16, 144, 72, 48, 1, 256, 16, 324, 64, 108, 200, 484, 32, 64, 288, 16, 144, 784, 96, 900, 1, 300, 512, 180, 32, 1296, 648, 432, 128, 1600, 216, 1764, 400, 144, 968, 2116, 64, 216, 128, 768, 576, 2704, 32, 500, 288, 972, 1568
Offset: 1

Views

Author

N. J. A. Sloane, Feb 11 2022

Keywords

Links

Crossrefs

Inspired by A351168.
Cf. A351425.

Programs

  • Mathematica
    a[n_] := Module[{f = FactorInteger[n]}, n*(f[[-1, 1]] - 1)^(f[[-1, 2]] + 1)/f[[-1, 1]]^f[[-1, 2]]]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Feb 11 2022 *)

A351425 If n = p_1^e_1 * ... * p_k^e_k, where p_1 < ... < p_k are primes, then a(n) is obtained by replacing the last factor p_k^e_k by (p_k + 1)^(e_k - 1); a(1) = 1.

Original entry on oeis.org

1, 1, 1, 3, 1, 2, 1, 9, 4, 2, 1, 4, 1, 2, 3, 27, 1, 8, 1, 4, 3, 2, 1, 8, 6, 2, 16, 4, 1, 6, 1, 81, 3, 2, 5, 16, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 8, 12, 3, 4, 1, 32, 5, 8, 3, 2, 1, 12, 1, 2, 9, 243, 5, 6, 1, 4, 3, 10, 1, 32, 1, 2, 18, 4, 7, 6, 1, 16, 64, 2
Offset: 1

Views

Author

Amiram Eldar and N. J. A. Sloane, Feb 11 2022

Keywords

Links

Crossrefs

Cf. A351168, A351419.

Programs

  • Mathematica
    a[n_] := Module[{f = FactorInteger[n]}, n*(f[[-1, 1]] + 1)^(f[[-1, 2]] - 1)/f[[-1, 1]]^f[[-1, 2]]]; a[1] = 1; Array[a, 100]
Showing 1-3 of 3 results.

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

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