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

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Greatest Prime Factor

Formula

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

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

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 *)

Prog

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

Crossrefs

Cf. A002808, A006530, A085392, A087040.

Cf. A027746, A052126.

Sequence in context: A327979 A107286 A339791 * A102096 A322813 A366189

Adjacent sequences: A087036 A087037 A087038 * A087040 A087041 A087042

Keyword

nonn,easy

Author

Reinhard Zumkeller, Aug 01 2003

Status

approved