A053143 Smallest square divisible by n.

1, 4, 9, 4, 25, 36, 49, 16, 9, 100, 121, 36, 169, 196, 225, 16, 289, 36, 361, 100, 441, 484, 529, 144, 25, 676, 81, 196, 841, 900, 961, 64, 1089, 1156, 1225, 36, 1369, 1444, 1521, 400, 1681, 1764, 1849, 484, 225, 2116, 2209, 144, 49, 100, 2601, 676, 2809

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Henry Bottomley, Some Smarandache-type multiplicative sequences.

Formula

a(n) = n*A007913(n) = A019554(n)^2 = n^2/A008833(n) = (n/A000188(n))^2.

Multiplicative with p^e -> p^(e + e mod 2), p prime. - Reinhard Zumkeller, Feb 09 2003

Dirichlet g.f.: zeta(2s-2)*zeta(s-2)/zeta(2s-4). - R. J. Mathar, Oct 31 2011

Sum_{k=1..n} a(k) ~ Pi^2 * n^3 / 45. - Vaclav Kotesovec, Feb 08 2019

Sum_{n>=1} 1/a(n) = 5/2. - Amiram Eldar, Jul 29 2022

Mathematica

Table[i = 1; While[Mod[i^2, n] > 0, i++]; i^2, {n, 100}] (* T. D. Noe, Oct 30 2011 *)
f[p_, e_] := p^(e + Mod[e, 2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Aug 29 2019 *)

Prog

(PARI) a(n) = n*core(n); /* Joerg Arndt, Aug 02 2012 */

Crossrefs

Cf. A000188, A007913, A008833, A019554.

Sequence in context: A197863 A087320 A087321 * A068238 A280441 A255290

Adjacent sequences: A053140 A053141 A053142 * A053144 A053145 A053146

Keyword

easy,nonn,mult

Author

Henry Bottomley, Feb 28 2000

Status

approved