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.

A355038 a(n) = n^2 times the squarefree kernel of n.

Original entry on oeis.org

1, 8, 27, 32, 125, 216, 343, 128, 243, 1000, 1331, 864, 2197, 2744, 3375, 512, 4913, 1944, 6859, 4000, 9261, 10648, 12167, 3456, 3125, 17576, 2187, 10976, 24389, 27000, 29791, 2048, 35937, 39304, 42875, 7776, 50653, 54872, 59319, 16000, 68921, 74088, 79507, 42592, 30375
Offset: 1

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Author

Peter Munn, Jun 16 2022

Keywords

Crossrefs

The range of values is A335988.

Programs

  • Mathematica
    a[n_] := n^2 * Times @@ FactorInteger[n][[;; , 1]]; Array[a, 50] (* Amiram Eldar, Jun 18 2022 *)
  • PARI
    a(n) = n^2 * factorback(factor(n)[,1]);

Formula

Multiplicative with a(p^e) = p^(2e+1).
a(n) = n^2 * A007947(n).
a(n) = A064549(n^2). - Amiram Eldar, Jun 20 2022
Sum_{k=1..n} a(k) ~ c * n^4, where c = (1/4) * Product_{p prime} (1 - 1/(p*(p+1))) = A065463 / 4 = 0.1761105502... . - Amiram Eldar, Nov 13 2022
a(n) = A356191(n^2). - Amiram Eldar, Nov 30 2023