A058035 Largest 4th-power-free number dividing n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 8, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 24, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 8, 65, 66, 67, 68, 69, 70, 71, 72

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

Cf. A007947, A007948, A008835, A046100, A053165, A065466.

Cf. A027748, A124010.

Sequence in context: A338782 A291580 A291581 * A366994 A365683 A057946

Adjacent sequences: A058032 A058033 A058034 * A058036 A058037 A058038

Keyword

easy,nonn,mult

Author

Henry Bottomley, Nov 16 2000

Status

approved