OFFSET
1,2
COMMENTS
The prime signature of a(n) is not determined by the prime signature of n. For example, a(2^3*3^5) = 2^3*3^6, but a(2^3*5^5) = 2^5*5^5. - David Wasserman, May 03 2005
Likewise, this sequence is not multiplicative. The smallest exception is a(24) = 144 > 72 = a(3)*a(8). - Franklin T. Adams-Watters, Oct 18 2011
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
a(n)/n <= A007947(n) (the squarefree kernel of n).
a(p^k) = p^k, a(k) = A007947(k)^2 for cubefree k. Furthermore, the upper bound on a(n)/n can be tightened to A007913(n). - Charlie Neder, Dec 26 2018
From Amiram Eldar, Jul 09 2022: (Start)
a(n) = n iff n is in A001597.
a(n) = n * A160400(n). (End)
EXAMPLE
a(54) = 216 = 6^3. 54 is the least n such that a(n)/n does not divide A007947(n).
MATHEMATICA
a[n_] := n * SelectFirst[Range[n], GCD @@ FactorInteger[n*#][[;; , 2]] > 1 &]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Amarnath Murthy, Sep 03 2003
EXTENSIONS
Edited and extended by David Wasserman, May 03 2005
STATUS
approved