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A073353
Sum of n and its squarefree kernel.
9
2, 4, 6, 6, 10, 12, 14, 10, 12, 20, 22, 18, 26, 28, 30, 18, 34, 24, 38, 30, 42, 44, 46, 30, 30, 52, 30, 42, 58, 60, 62, 34, 66, 68, 70, 42, 74, 76, 78, 50, 82, 84, 86, 66, 60, 92, 94, 54, 56, 60, 102, 78, 106, 60, 110, 70, 114, 116, 118, 90, 122, 124, 84, 66, 130, 132
OFFSET
1,1
COMMENTS
a(n) is even; a(n)=2*n iff n is squarefree.
Least k >n such that n divides k^n. - Benoit Cloitre, Oct 09 2002
a(n) is the smallest integer > n such that the positive integers coprime to a(n) are also coprime to n. - Leroy Quet, Dec 24 2006
LINKS
FORMULA
a(n) = n + A007947(n).
Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 + A065463 = 1.704442... . - Amiram Eldar, Dec 07 2023
MATHEMATICA
a[n_] := n + Times @@ FactorInteger[n][[;; , 1]]; Array[a, 100] (* Amiram Eldar, Dec 07 2023 *)
PROG
(Haskell)
a073353 n = n + a007947 n -- Reinhard Zumkeller, Jul 23 2013
(PARI) a(n)=vecprod(factor(n)[, 1])+n \\ Charles R Greathouse IV, Nov 05 2017
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Jul 29 2002
STATUS
approved