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
Examples
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).
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- Henry Bottomley, Some Smarandache-type multiplicative sequences.
Programs
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Haskell
a058035 n = product $ zipWith (^) (a027748_row n) (map (min 3) $ a124010_row n) -- Reinhard Zumkeller, Jan 06 2012
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Mathematica
f[p_, e_] := p^Min[e, 3]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)
-
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
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