Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #34 Jun 18 2022 04:04:09
%S 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 21,22,15,23,24,7,25,17,26,27,11,28,19,29,30,31,21,32,13,33,34,23,35,
%U 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 Largest proper divisor of the n-th composite number.
%C Old name: The n-th positive composite number divided by its lowest nontrivial factor.
%H K. Stern, <a href="/A160180/b160180.txt">Table of n, a(n) for n = 1..9999</a>
%F a(n) = A032742(A002808(n)) = A002808(n) / A056608(n) = A163870(n,A144925(n)). - _Reinhard Zumkeller_, Mar 29 2014
%e 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 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 Divisors[#][[-2]]&/@Select[Range[200],CompositeQ] (* _Harvey P. Dale_, Dec 06 2021 *)
%t (# / FactorInteger[#][[1, 1]])& /@ Select[Range[300], CompositeQ] (* _Amiram Eldar_, Jun 18 2022 *)
%o (MATLAB)
%o 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 (Haskell)
%o a160180 = a032742 . a002808 -- _Reinhard Zumkeller_, Mar 29 2014
%Y Cf. A002808, A032742, A056608, A163870, A144925.
%K easy,nonn
%O 1,1
%A _Kyle Stern_, May 03 2009, May 04 2009
%E Indices of b-file corrected, more terms added using b-file. - _N. J. A. Sloane_, Aug 31 2009
%E New name from _Reinhard Zumkeller_, Mar 29 2014
%E Incorrect formula removed by _Ridouane Oudra_, Oct 15 2021