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%I #45 Oct 13 2022 05:57:05
%S 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,
%T 9,28,29,30,31,4,33,34,35,36,37,38,39,20,41,42,43,44,45,46,47,12,49,
%U 50,51,52,53,18,55,28,57,58,59,60,61,62,63,4,65,66,67,68,69,70,71,36,73
%N Largest cubefree number dividing n.
%H Reinhard Zumkeller, <a href="/A007948/b007948.txt">Table of n, a(n) for n = 1..10000</a>
%H Henry Bottomley, <a href="http://www.gallup.unm.edu/~smarandache/Bottomley-Sm-Mult-Functions.htm">Some Smarandache-type multiplicative functions</a>.
%H Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>, 1993.
%F Multiplicative with a(p^e) = p^(min(e, 2)). - _David W. Wilson_, Aug 01 2001
%F a(n) = max{A212793(A027750(n,k)) * A027750(n,k): k=1..A000005(n)}. - _Reinhard Zumkeller_, May 27 2012
%F a(n) = A071773(n)*A007947(n). - observed by _Velin Yanev_, Aug 20 2017, confirmed by _Antti Karttunen_, Nov 28 2017
%F a(n) = n / A062378(n) = n / A003557(A003557(n)). - _Antti Karttunen_, Nov 28 2017
%F Sum_{k=1..n} a(k) ~ (1/2) * c * n^2, where c = Product_{p prime} (1 - 1/(p^2*(p+1))) = 0.881513... (A065465). - _Amiram Eldar_, Oct 13 2022
%t Table[Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 0 :> p^Min[e, 2]], {n, 73}] (* _Michael De Vlieger_, Jul 18 2017 *)
%o (Haskell)
%o a007948 = last . filter ((== 1) . a212793) . a027750_row
%o -- _Reinhard Zumkeller_, May 27 2012, Jan 06 2012
%o (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
%o (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
%Y Cf. A003557, A004709, A007947, A027748, A058035, A062378, A065465, A124010, A197863.
%K nonn,mult
%O 1,2
%A R. Muller
%E More terms from _Henry Bottomley_, Jun 18 2001
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