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A055491 Smallest square divisible by n divided by largest square which divides n. 2
1, 4, 9, 1, 25, 36, 49, 4, 1, 100, 121, 9, 169, 196, 225, 1, 289, 4, 361, 25, 441, 484, 529, 36, 1, 676, 9, 49, 841, 900, 961, 4, 1089, 1156, 1225, 1, 1369, 1444, 1521, 100, 1681, 1764, 1849, 121, 25, 2116, 2209, 9, 1, 4, 2601, 169, 2809, 36, 3025, 196, 3249, 3364 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Henry Bottomley, Some Smarandache-type multiplicative sequences.

FORMULA

If n is written as Product(Pj^Ej) then a(n) = Product(Pj^(2*(Ej mod 2))).

a(n) = A053143(n)/A008833(n) = A007913(n)^2 = (A019554(n)/A000188(n))^2 = A000290(n)/A008833(n)^2.

EXAMPLE

a(12) = 36/4 = 9.

MATHEMATICA

With[{sqs=Range[100]^2}, Table[SelectFirst[sqs, Divisible[#, n]&]/ SelectFirst[ Reverse[sqs], Divisible[n, #]&], {n, 60}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 18 2018 *)

f[p_, e_] := p^(2 * Mod[e, 2]); a[n_] := Times @@ (f @@@ FactorInteger[n]); Array[a, 100] (* Amiram Eldar, Sep 07 2020 *)

PROG

(Haskell)

a055491 = (^ 2) . a007913  -- Reinhard Zumkeller, Jul 23 2014

CROSSREFS

Cf. A056551, A056552.

Cf. A000188, A000290, A007913, A008833, A019554, A053143.

Sequence in context: A236104 A152205 A129861 * A032523 A032760 A129970

Adjacent sequences:  A055488 A055489 A055490 * A055492 A055493 A055494

KEYWORD

easy,nonn,mult

AUTHOR

Henry Bottomley, Jun 28 2000

STATUS

approved

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Last modified May 18 11:30 EDT 2021. Contains 343995 sequences. (Running on oeis4.)