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For any n > 0: start with x = n; for k = 1..n, if k divides x then divide x by k; a(n) corresponds to the final value of x.
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%I #10 Apr 19 2020 05:21:46

%S 1,1,1,2,1,1,1,1,3,1,1,2,1,1,1,2,1,3,1,2,1,1,1,1,5,1,1,2,1,1,1,4,1,1,

%T 1,1,1,1,1,1,1,1,1,2,3,1,1,2,7,5,1,2,1,1,1,1,1,1,1,2,1,1,3,1,1,1,1,2,

%U 1,1,1,3,1,1,5,2,1,1,1,2,3,1,1,2,1,1,1

%N For any n > 0: start with x = n; for k = 1..n, if k divides x then divide x by k; a(n) corresponds to the final value of x.

%C Every integer appears infinitely many times in this sequence.

%H Rémy Sigrist, <a href="/A334039/b334039.txt">Table of n, a(n) for n = 1..10000</a>

%F a(s) = 1 for any squarefree number s.

%F a(p^2) = p for any prime number p.

%F a(p^k) = p^A002262(k) for any k >= 0 and prime number p.

%F a(n!) = 1 for any n >= 0.

%F a(n! * k) = k for any n >= 1 and k = 1..n.

%o (PARI) a(n) = { fordiv (n, d, if (n%d==0, n\=d); if (n<=d, return (n))) }

%Y Cf. A002262.

%K nonn

%O 1,4

%A _Rémy Sigrist_, Apr 13 2020