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A160180 Largest proper divisor of the n-th composite number.

%I A160180 #34 Jun 18 2022 04:04:09
%S A160180 2,3,4,3,5,6,7,5,8,9,10,7,11,12,5,13,9,14,15,16,11,17,7,18,19,13,20,
%T A160180 21,22,15,23,24,7,25,17,26,27,11,28,19,29,30,31,21,32,13,33,34,23,35,
%U A160180 36,37,25,38,11,39,40,27,41,42,17,43,29,44,45,13,46,31,47,19,48,49,33,50,51,52
%N A160180 Largest proper divisor of the n-th composite number.
%C A160180 Old name: The n-th positive composite number divided by its lowest nontrivial factor.
%H A160180 K. Stern, <a href="/A160180/b160180.txt">Table of n, a(n) for n = 1..9999</a>
%F A160180 a(n) = A032742(A002808(n)) = A002808(n) / A056608(n) = A163870(n,A144925(n)). - _Reinhard Zumkeller_, Mar 29 2014
%e A160180 a(1) = 4/2 = 2, a(2) = 6/2 = 3, a(3) = 8/2 = 4, a(4) = 9/3 = 3, a(5) = 10/2 = 5.
%t A160180 f[n_] := Block[{k = n + PrimePi@ n + 1}, While[k != n + PrimePi@ k + 1, k++ ]; k/FactorInteger[k][[1, 1]]]; Array[f, 75] (* _Robert G. Wilson v_, May 11 2012 *)
%t A160180 Divisors[#][[-2]]&/@Select[Range[200],CompositeQ] (* _Harvey P. Dale_, Dec 06 2021 *)
%t A160180 (# / FactorInteger[#][[1, 1]])& /@ Select[Range[300], CompositeQ] (* _Amiram Eldar_, Jun 18 2022 *)
%o A160180 (MATLAB)
%o A160180 function [a] = A160180(k) j = 0; n = 1; while j < k if isprime(n) == 1 skip elseif isprime(n) == 0 j = j + 1; factors = factor(n); lowfactor = factors(1,1); a(j,1) = n/lowfactor; end n = n + 1; end - _Kyle Stern_, May 04 2009
%o A160180 (Haskell)
%o A160180 a160180 = a032742 . a002808  -- _Reinhard Zumkeller_, Mar 29 2014
%Y A160180 Cf. A002808, A032742, A056608, A163870, A144925.
%K A160180 easy,nonn
%O A160180 1,1
%A A160180 _Kyle Stern_, May 03 2009, May 04 2009
%E A160180 Indices of b-file corrected, more terms added using b-file. - _N. J. A. Sloane_, Aug 31 2009
%E A160180 New name from _Reinhard Zumkeller_, Mar 29 2014
%E A160180 Incorrect formula removed by _Ridouane Oudra_, Oct 15 2021