A007948 Largest cubefree number dividing n.

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

Offset

1,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Henry Bottomley, Some Smarandache-type multiplicative functions.

Florentin Smarandache, Only Problems, Not Solutions!, 1993.

Formula

Multiplicative with a(p^e) = p^(min(e, 2)). - David W. Wilson, Aug 01 2001

a(n) = max{A212793(A027750(n,k)) * A027750(n,k): k=1..A000005(n)}. - Reinhard Zumkeller, May 27 2012

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

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

Mathematica

Table[Apply[Times, FactorInteger[n] /. {p_, e_} /; p > 0 :> p^Min[e, 2]], {n, 73}] (* Michael De Vlieger, Jul 18 2017 *)

Prog

(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

Crossrefs

Cf. A003557, A004709, A007947, A027748, A058035, A062378, A065465, A124010, A197863.

Sequence in context: A319999 A083501 A007922 * A355261 A353897 A366905

Adjacent sequences: A007945 A007946 A007947 * A007949 A007950 A007951

Keyword

nonn,mult

Author

R. Muller

Extensions

More terms from Henry Bottomley, Jun 18 2001

Status

approved