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 A032742 a(1) = 1; for n > 1, a(n) = largest proper divisor of n. 202
 1, 1, 1, 2, 1, 3, 1, 4, 3, 5, 1, 6, 1, 7, 5, 8, 1, 9, 1, 10, 7, 11, 1, 12, 5, 13, 9, 14, 1, 15, 1, 16, 11, 17, 7, 18, 1, 19, 13, 20, 1, 21, 1, 22, 15, 23, 1, 24, 7, 25, 17, 26, 1, 27, 11, 28, 19, 29, 1, 30, 1, 31, 21, 32, 13, 33, 1, 34, 23, 35, 1, 36, 1, 37, 25, 38, 11, 39, 1, 40 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS It seems that a(n) = Max{gcd(n,j); j=n+1..2n-1}. - Labos Elemer, May 22 2002 This is correct: No integer in the range [n+1, 2n-1] has n as its divisor, but certainly at least one multiple of the largest proper divisor of n will occur there (e.g., if it is n/2, then at n + (n/2)). - Antti Karttunen, Dec 18 2014 LINKS Rémi Eismann, Table of n, a(n) for n=1..10000 (first 1000 terms from T. D. Noe) Eric Weisstein's World of Mathematics, Proper Divisor FORMULA a(n) = n / A020639(n). Other identities and observations: A054576(n) = a(a(n)); A117358(n) = a(a(a(n))) = a(A054576(n)); a(A008578(n)) = 1, a(A002808(n)) > 1. - Reinhard Zumkeller, Mar 10 2006 a(n) = A130064(n) / A006530(n). - Reinhard Zumkeller, May 05 2007 a(m)*a(n) < a(m*n) for m and n > 1. - Reinhard Zumkeller, Apr 11 2008 a(m*n) = max(m*a(n), n*a(m)). - Robert Israel, Dec 18 2014 From Antti Karttunen, Mar 31 2018: (Start) a(n) = n - A060681(n). For n > 1, a(n) = A003961^(r)(A246277(n)), where r = A055396(n)-1 and A003961^(r)(n) stands for shifting the prime factorization of n by r positions towards larger primes. a(n) = A250246(A302042(A250245(n))) = A302026(A302032(A302025(n))). For all n >= 1, A276085(a(A276086(n))) = A276151(n). (End) MAPLE A032742 :=proc(n) option remember; if n = 1 then 1; else numtheory[divisors](n) minus {n} ; max(op(%)) ; end if; end proc: # R. J. Mathar, Jun 13 2011 1, seq(n/min(numtheory:-factorset(n)), n=2..1000); # Robert Israel, Dec 18 2014 MATHEMATICA f[n_] := If[n == 1, 1, Divisors[n][[-2]]]; Table[f[n], {n, 100}] (* Vladimir Joseph Stephan Orlovsky, Mar 03 2010 *) Join[{1}, Divisors[#][[-2]]&/@Range[2, 80]] (* Harvey P. Dale, Nov 29 2011 *) PROG (PARI) a(n)=if(n==1, 1, n/factor(n)[1, 1]) \\ Charles R Greathouse IV, Jun 15 2011 (Haskell) a032742 n = n `div` a020639 n  -- Reinhard Zumkeller, Oct 03 2012 (Scheme) (define (A032742 n) (/ n (A020639 n))) ;; Antti Karttunen, Dec 18 2014 CROSSREFS Equals n/A020639(n). Cf. A032741, A052126, A055396, A060681, A068319, A063928, A246277, A286477, A300236, A302032, A302042, A325563, A325567. Sequence in context: A325641 A325563 A159353 * A060654 A291329 A291328 Adjacent sequences:  A032739 A032740 A032741 * A032743 A032744 A032745 KEYWORD nonn,easy,nice AUTHOR Patrick De Geest, May 15 1998 STATUS approved

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Last modified July 1 23:45 EDT 2020. Contains 335389 sequences. (Running on oeis4.)