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%I #24 Dec 07 2023 01:45:23
%S 2,4,6,6,10,12,14,10,12,20,22,18,26,28,30,18,34,24,38,30,42,44,46,30,
%T 30,52,30,42,58,60,62,34,66,68,70,42,74,76,78,50,82,84,86,66,60,92,94,
%U 54,56,60,102,78,106,60,110,70,114,116,118,90,122,124,84,66,130,132
%N Sum of n and its squarefree kernel.
%C a(n) is even; a(n)=2*n iff n is squarefree.
%C Least k >n such that n divides k^n. - _Benoit Cloitre_, Oct 09 2002
%C 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
%H Reinhard Zumkeller, <a href="/A073353/b073353.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n + A007947(n).
%F Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 1 + A065463 = 1.704442... . - _Amiram Eldar_, Dec 07 2023
%t a[n_] := n + Times @@ FactorInteger[n][[;;, 1]]; Array[a, 100] (* _Amiram Eldar_, Dec 07 2023 *)
%o (Haskell)
%o a073353 n = n + a007947 n -- _Reinhard Zumkeller_, Jul 23 2013
%o (PARI) a(n)=vecprod(factor(n)[,1])+n \\ _Charles R Greathouse IV_, Nov 05 2017
%Y Cf. A007947, A005117, A065463, A066503, A064549, A003557, A073354, A078310.
%K nonn,easy
%O 1,1
%A _Reinhard Zumkeller_, Jul 29 2002
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