%I #17 Jul 13 2021 06:24:15
%S 1,2,3,2,5,7,11,2,3,13,17,19,23,29,31,2,37,41,43,47,53,59,61,67,5,71,
%T 3,73,79,83,89,2,97,101,103,107,109,113,127,131,137,139,149,151,157,
%U 163,167,173,7,179,181,191,193,197,199,211,223,227,229,233,239,241
%N For n > 1: a(n) = p if n = p^e with p prime and e > 1, otherwise a(n) = (n-m)-th prime, where m = number of nonprime prime powers <= n; a(1)=1.
%C a(n) = A025473(n) if n = p^e with p prime and e > 1, otherwise a(n) = A008578(n-A085501(n));
%C n divides A085819(n) = Product_{k<=n} a(k), as by construction: a(1)=1; if n divides A085819(n-1) then a(n) = smallest prime not occurring earlier; if n does not divide A085819(n-1) then a(n) = greatest prime factor of n (A006530);
%C A000040 occurs infinitely many times as a subsequence.
%C a(A085971(n))=A000040(n) and for all k > 1: a(A000040(n)^k)=A000040(n); A085985(n)=A049084(a(n)). - _Reinhard Zumkeller_, Jul 06 2003
%H Michel Marcus, <a href="/A085818/b085818.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) f(n) = 1 + sum(k=2, n, isprimepower(k) && !isprime(k)); \\ A085501
%o a(n) = {if (n==1, return (1)); my(p); if (isprimepower(n, &p) && !isprime(n), p, prime(n-f(n)));} \\ _Michel Marcus_, Jan 28 2021
%Y Cf. A000040, A008578, A085971.
%Y Cf. A006530, A025473, A085501, A085819, A085985, A049084.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Jul 04 2003
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