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.

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A369430 Smallest number whose square is divisible by the n-th powerful number.

Original entry on oeis.org

1, 2, 4, 3, 4, 5, 9, 8, 6, 7, 8, 12, 9, 10, 18, 11, 25, 16, 12, 13, 14, 20, 36, 15, 27, 16, 24, 17, 18, 49, 19, 28, 20, 36, 21, 22, 50, 32, 23, 24, 25, 36, 45, 26, 27, 28, 40, 29, 72, 30, 31, 44, 54, 100, 32, 33, 75, 48, 34, 35, 36, 63, 121, 52, 37, 98, 38, 39
Offset: 1

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Author

Amiram Eldar, Jan 23 2024

Keywords

Crossrefs

Programs

  • Mathematica
    f[p_, e_] := p^Ceiling[e/2]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; s /@ Select[Range[2000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]
    (* or *)
    f[p_, e_] := p^Ceiling[e/2]; f[p_, 1] := 0; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 2000], # > 0 &]
  • PARI
    s(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i,2] == 1, 0, f[i,1]^ceil(f[i,2]/2)));}
    lista(kmax) = {my(s1); for(k = 1, kmax, s1 = s(k); if(s1 > 0, print1(s1, ", ")));}

Formula

a(n) = A019554(A001694(n)).
a(n) > 1 for n >= 2.
Sum_{k=1..n} a(k) ~ (c*n/Pi)^2 * (2*log(n) + 2*log(c) + 5*gamma - 1 - 6*zeta'(2)/zeta(2)), where gamma is Euler's constant (A001620), and c = zeta(3)/zeta(3/2).
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