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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Aug 01 2003

Keywords

• nonn

Comments

a(n) = A087039(A002808(n));

a(n) = A006530(A002808(n)/A052369(n)).

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A006530, A052369, A087039.

Programs

Maple

f:= proc(n) local F;
  if isprime(n) then return NULL fi;
  F:= sort(ifactors(n)[2],(a,b) -> a[1]>b[1]);
  if F[1][2] >= 2 then F[1][1] else F[2][1] fi
end proc:
map(f, [$2..200]); # Robert Israel, Feb 20 2024

Mathematica

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 *)