OFFSET
1,2
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
FORMULA
Multiplicative with a(p^e) = p ^ min(e,3), p prime, e > 0. - Reinhard Zumkeller, Jan 06 2012
Sum_{k=1..n} a(k) ~ (1/2) * c * n^2, where c = Product_{p prime} (1 - 1/(p^3*(p+1))) = 0.947733... (A065466). - Amiram Eldar, Oct 13 2022
EXAMPLE
a(96) = 24 since the factors of 96 are {1,2,3,4,6,8,12,16,24,32,48,96} but 32, 48 and 96 all contain a 4th power factor (16).
MATHEMATICA
f[p_, e_] := p^Min[e, 3]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)
PROG
(Haskell)
a058035 n = product $
zipWith (^) (a027748_row n) (map (min 3) $ a124010_row n)
-- Reinhard Zumkeller, Jan 06 2012
(PARI) a(n) = my(f=factor(n)); for(k=1, #f~, f[k, 2]=min(3, f[k, 2])); factorback(f); \\ Michel Marcus, Sep 13 2017
CROSSREFS
KEYWORD
easy,nonn,mult
AUTHOR
Henry Bottomley, Nov 16 2000
STATUS
approved