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 A085818 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. 4
 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, 3, 73, 79, 83, 89, 2, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 7, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = A025473(n) if n = p^e with p prime and e > 1, otherwise a(n) = A008578(n-A085501(n)); 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); A000040 occurs infinitely many times as a subsequence. 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 LINKS Michel Marcus, Table of n, a(n) for n = 1..10000 PROG (PARI) f(n) = 1 + sum(k=2, n, isprimepower(k) && !isprime(k)); \\ A085501 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 CROSSREFS Cf. A000040, A008578, A085971. Cf. A006530, A025473, A085501, A085819, A085985, A049084. Sequence in context: A058977 A337246 A347104 * A270709 A323382 A064939 Adjacent sequences: A085815 A085816 A085817 * A085819 A085820 A085821 KEYWORD nonn AUTHOR Reinhard Zumkeller, Jul 04 2003 STATUS approved

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Last modified March 30 09:39 EDT 2023. Contains 361609 sequences. (Running on oeis4.)