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))).
Sum_{k=1..n} a(k) ~ c * n^3, where c = (zeta(6)/(3*zeta(2))) = 2*Pi^4/945 = 0.206156... . - Amiram Eldar, Oct 27 2022
Dirichlet g.f.: zeta(s-2) * zeta(2*s) / zeta(2*s-4). - Amiram Eldar, Sep 16 2023
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
(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i, 1]^(2*(f[i, 2]%2))); } \\ Amiram Eldar, Oct 27 2022
CROSSREFS
KEYWORD
easy,nonn,mult
AUTHOR
Henry Bottomley, Jun 28 2000
STATUS
approved