The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A085818 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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.
(history; published version)

#21 by Michael De Vlieger at Tue Aug 20 13:19:32 EDT 2024

STATUS

reviewed

approved

#20 by Michel Marcus at Tue Aug 20 12:32:06 EDT 2024

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proposed

reviewed

#19 by Chai Wah Wu at Tue Aug 20 12:30:12 EDT 2024

STATUS

editing

proposed

#18 by Chai Wah Wu at Tue Aug 20 12:30:09 EDT 2024

PROG

(Python)

from sympy import primefactors, prime, primepi, integer_nthroot

def A085818(n): return 1 if n==1 else (f[0] if len(f:=primefactors(n))==1 and f[0]<n else prime(n-1-sum(primepi(integer_nthroot(n, k)[0]) for k in range(2, n.bit_length())))) # Chai Wah Wu, Aug 20 2024

STATUS

approved

editing

#17 by Bruno Berselli at Tue Jul 13 06:24:15 EDT 2021

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proposed

approved

#16 by Michel Marcus at Tue Jul 13 05:35:00 EDT 2021

STATUS

editing

proposed

#15 by Michel Marcus at Tue Jul 13 05:33:11 EDT 2021

LINKS

Michel Marcus, <a href="/A085818/b085818.txt">Table of n, a(n) for n = 1..10000</a>

STATUS

approved

editing

#14 by Susanna Cuyler at Tue Feb 02 22:15:27 EST 2021

STATUS

proposed

approved

#13 by Jon E. Schoenfield at Tue Feb 02 19:13:06 EST 2021

STATUS

editing

proposed

#12 by Jon E. Schoenfield at Tue Feb 02 19:13:04 EST 2021

NAME

For n > 1: a(n) = p if (n = p^e with p prime and e > 1, otherwise a(n) then p else = (n-m)-th prime, where m = number of nonprime prime powers <= n; a(1)=1.

COMMENTS

a(n) = A025473(n) if (n = p^e with p prime and e > 1) then A025473, otherwise a(n) else = A008578(n-A085501(n));

n divides A085819(n) =Prod(a(k): 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);

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

STATUS

approved

editing