A087039 If n is prime then 1 else 2nd largest prime factor of n.

1, 1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 5, 2, 3, 2, 1, 3, 1, 2, 3, 2, 5, 3, 1, 2, 3, 2, 1, 3, 1, 2, 3, 2, 1, 2, 7, 5, 3, 2, 1, 3, 5, 2, 3, 2, 1, 3, 1, 2, 3, 2, 5, 3, 1, 2, 3, 5, 1, 3, 1, 2, 5, 2, 7, 3, 1, 2, 3, 2, 1, 3, 5, 2, 3, 2, 1, 3, 7, 2, 3, 2, 5, 2, 1, 7, 3, 5, 1, 3

Offset: 1

Author

Reinhard Zumkeller, Aug 01 2003

Keywords

• nonn
• easy

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Greatest Prime Factor

Crossrefs

Cf. A002808, A006530, A085392, A087040.

Cf. A027746, A052126.

Programs

Haskell

a087039 n | null ps   = 1
          | otherwise = head ps
          where ps = tail $ reverse $ a027746_row n
-- Reinhard Zumkeller, Oct 03 2012

Maple

A087039 := proc(n)
    local pset ,t;
    if isprime(n) or n= 1 then
        1;
    else
        pset := [] ;
        for p in ifactors(n)[2] do
            pset := [op(pset),seq(op(1,p),t=1..op(2,p))] ;
        end do:
        op(-2,sort(pset)) ;
    end if;
end proc: # R. J. Mathar, Sep 14 2012

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]];
a[n_] := If[PrimeQ[n], 1, gpf[n/gpf[n]]];
Array[a, 105] (* Jean-François Alcover, Dec 16 2021 *)

Python

from sympy import factorint
def a(n):
    pf = factorint(n, multiple=True)
    return 1 if len(pf) < 2 else pf[-2]
print([a(n) for n in range(1, 103)]) # Michael S. Branicky, Dec 16 2021

Formula

a(n) = A006530(A052126(n)) = A006530(n/A006530(n));

A087040(n) = a(A002808(n)).