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A087040 2nd largest prime factor of n-th composite number.

%I A087040 #12 Feb 21 2024 08:27:18
%S A087040 2,2,2,3,2,2,2,3,2,3,2,3,2,2,5,2,3,2,3,2,3,2,5,3,2,3,2,3,2,3,2,2,7,5,
%T A087040 3,2,3,5,2,3,2,3,2,3,2,5,3,2,3,5,3,2,5,2,7,3,2,3,2,3,5,2,3,2,3,7,2,3,
%U A087040 2,5,2,7,3,5,3,2,5,2,3,5,3,2,3,5,2,3,2,7,3,11,2,3,2,5,3,2,3,5,3,7,2,3
%N A087040 2nd largest prime factor of n-th composite number.
%C A087040 a(n) = A087039(A002808(n));
%C A087040 a(n) = A006530(A002808(n)/A052369(n)).
%H A087040 Robert Israel, <a href="/A087040/b087040.txt">Table of n, a(n) for n = 1..10000</a>
%p A087040 f:= proc(n) local F;
%p A087040   if isprime(n) then return NULL fi;
%p A087040   F:= sort(ifactors(n)[2],(a,b) -> a[1]>b[1]);
%p A087040   if F[1][2] >= 2 then F[1][1] else F[2][1] fi
%p A087040 end proc:
%p A087040 map(f, [$2..200]); # _Robert Israel_, Feb 20 2024
%t A087040 Table[l=FactorInteger[ResourceFunction["Composite"][n]];If[Last[l][[2]]>1,Last[l][[1]],First[Part[l,-2]]],{n,102}] (* _James C. McMahon_, Feb 20 2024 *)
%Y A087040 Cf. A002808, A006530, A052369, A087039.
%K A087040 nonn
%O A087040 1,1
%A A087040 _Reinhard Zumkeller_, Aug 01 2003