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A007948
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Largest cubefree number dividing n.
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17
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1, 2, 3, 4, 5, 6, 7, 4, 9, 10, 11, 12, 13, 14, 15, 4, 17, 18, 19, 20, 21, 22, 23, 12, 25, 26, 9, 28, 29, 30, 31, 4, 33, 34, 35, 36, 37, 38, 39, 20, 41, 42, 43, 44, 45, 46, 47, 12, 49, 50, 51, 52, 53, 18, 55, 28, 57, 58, 59, 60, 61, 62, 63, 4, 65, 66, 67, 68, 69, 70, 71, 36, 73
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OFFSET
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1,2
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COMMENTS
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a(n) = max{A212793(A027750(n,k)) * A027750(n,k): k=1..A000005(n)}. - Reinhard Zumkeller, May 27 2012
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
H. Bottomley, Some Smarandache-type multiplicative functions.
F. Smarandache, Only Problems, Not Solutions!.
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FORMULA
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Multiplicative with a(p^e) = p^(min(e, 2)). - David W. Wilson, Aug 01 2001
a(n) = A071773(n)*A007947(n). - observed by Velin Yanev, Aug 20 2017, confirmed by Antti Karttunen, Nov 28 2017
a(n) = n / A062378(n) = n / A003557(A003557(n)). - Antti Karttunen, Nov 28 2017
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MATHEMATICA
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Table[Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 0 :> p^Min[e, 2]], {n, 73}] (* Michael De Vlieger, Jul 18 2017 *)
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PROG
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(Haskell)
a007948 = last . filter ((== 1) . a212793) . a027750_row
-- Reinhard Zumkeller, May 27 2012, Jan 06 2012
(PARI) a(n) = my(f=factor(n)); for (i=1, #f~, f[i, 2] = min(f[i, 2], 2)); factorback(f); \\ Michel Marcus, Jun 09 2014
(Scheme, with memoization-macro definec) (definec (A007948 n) (if (= 1 n) n (* (expt (A020639 n) (min 2 (A067029 n))) (A007948 (A028234 n))))) ;; Antti Karttunen, Nov 28 2017
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CROSSREFS
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Cf. A003557, A004709, A007947, A058035, A062378, A027748, A124010, A197863.
Sequence in context: A319999 A083501 A007922 * A038389 A058223 A245355
Adjacent sequences: A007945 A007946 A007947 * A007949 A007950 A007951
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KEYWORD
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nonn,mult
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AUTHOR
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R. Muller
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EXTENSIONS
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More terms from Henry Bottomley, Jun 18 2001
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STATUS
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approved
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