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A058035
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Largest 4th-power-free number dividing n.
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3
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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
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OFFSET
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1,2
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Henry Bottomley, Some Smarandache-type multiplicative sequences.
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FORMULA
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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
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EXAMPLE
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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).
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MATHEMATICA
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f[p_, e_] := p^Min[e, 3]; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jul 09 2022 *)
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PROG
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(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
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CROSSREFS
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Cf. A007947, A007948, A008835, A046100, A053165, A065466.
Cf. A027748, A124010.
Sequence in context: A338782 A291580 A291581 * A057946 A331270 A117657
Adjacent sequences: A058032 A058033 A058034 * A058036 A058037 A058038
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Henry Bottomley, Nov 16 2000
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STATUS
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approved
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