OFFSET
1,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
Multiplicative with a(p^e) = p^max(e,2).
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + (2*p-1)/(p^2*(p-1))) = 2.71098009471568319328... . - Amiram Eldar, Jul 29 2022
Sum_{k=1..n} a(k) ~ c * n^3, where c = (Pi^2/18) * Product_{p prime} (1 - 2/p^2 + 2/p^4 - 1/p^5) = 0.2165355664... . - Amiram Eldar, Nov 19 2022
a(n) = n * A055231(n). - Amiram Eldar, Sep 01 2023
MATHEMATICA
With[{pwrnos=Join[{1}, Select[Range[5000], Min[Transpose[ FactorInteger[#]] [[2]]]>1&]]}, Flatten[Table[Select[pwrnos, Divisible[#, n]&, 1], {n, 60}]]] (* Harvey P. Dale, Aug 14 2012 *)
f[p_, e_] := p^Max[e, 2]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)
PROG
(PARI) a(n)=local(fm=factor(n)); prod(k=1, matsize(fm)[1], fm[k, 1]^max(fm[k, 2], 2))
(Haskell)
a197863 n = product $
zipWith (^) (a027748_row n) (map (max 2) $ a124010_row n)
-- Reinhard Zumkeller, Jan 06 2012
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Franklin T. Adams-Watters, Oct 18 2011
STATUS
approved