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URL: https://oeis.org/A062759

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A062759
Largest power of squarefree kernel of n (= A007947) which divides n.
6
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 6, 13, 14, 15, 16, 17, 6, 19, 10, 21, 22, 23, 6, 25, 26, 27, 14, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 10, 41, 42, 43, 22, 15, 46, 47, 6, 49, 10, 51, 26, 53, 6, 55, 14, 57, 58, 59, 30, 61, 62, 21, 64, 65, 66, 67, 34, 69, 70, 71, 36, 73
OFFSET
1,2
COMMENTS
a(n) is a first power if and only if n is not a powerful number (A001694, A052485).
LINKS
FORMULA
a(n) = A007947(n)^A051904(n).
From Amiram Eldar, Feb 12 2023: (Start)
a(n) = n/A062759(n).
Sum_{k=1..n} a(k) ~ c * n^2, where c = A065463 / 2 = 0.352221... . (End)
EXAMPLE
n = 1800: squarefree kernel is 2*3*5 = 30 and a(1800) = 900 = 30^2 divides n, exponent of 30 is the smallest prime exponent of 1800 = 2*2*2*3*3*5*5.
MATHEMATICA
{1}~Join~Table[#^IntegerExponent[n, #] &@ Last@ Select[Divisors@ n, SquareFreeQ], {n, 2, 73}] (* Michael De Vlieger, Nov 02 2017 *)
a[n_] := Module[{f = FactorInteger[n], e}, e = Min[f[[;; , 2]]]; f[[;; , 2]] = e; Times @@ Power @@@ f]; Array[a, 100] (* Amiram Eldar, Feb 12 2023 *)
PROG
(Haskell)
a062759 n = a007947 n ^ a051904 n -- Reinhard Zumkeller, Jul 15 2012
(PARI) a(n) = {if(n==1, 1, my(f = factor(n), e = vecmin(f[, 2])); prod(i = 1, #f~, f[i, 1]^e)); } \\ Amiram Eldar, Feb 12 2023
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 16 2001
STATUS
approved