A117818 a(n) = n if n is 1 or a prime, otherwise a(n) = n divided by the least prime factor of n (A032742(n)).

1, 2, 3, 2, 5, 3, 7, 4, 3, 5, 11, 6, 13, 7, 5, 8, 17, 9, 19, 10, 7, 11, 23, 12, 5, 13, 9, 14, 29, 15, 31, 16, 11, 17, 7, 18, 37, 19, 13, 20, 41, 21, 43, 22, 15, 23, 47, 24, 7, 25, 17, 26, 53, 27, 11, 28, 19, 29, 59, 30, 61, 31, 21, 32, 13, 33, 67, 34, 23, 35, 71, 36, 73, 37, 25, 38

Offset: 1

Author

Roger L. Bagula, Apr 30 2006

Keywords

• nonn
• easy

Comments

A026741 generalized to give either a prime or the largest proper divisor of a nonprime.

Sometimes called "Conway's subprime function", although it surely predates John Conway. - N. J. A. Sloane, Sep 29 2017

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A026741, A032742, A292772.

Programs

Haskell

a117818 n = if a010051 n == 1 then n else a032742 n
-- Reinhard Zumkeller, Jun 24 2013

Maple

A117818 := proc(n)
    local a,d;
    if isprime(n) or n =1 then
        return n;
    end if;
    a := -1 ;
    for d in numtheory[divisors](n) do
        if d < n and d> a then
            a := d ;
        end if;
    end do:
    a ;
end proc:
seq(A117818(n),n=1..100) ; # R. J. Mathar, Apr 30 2024

Mathematica

Table[If[PrimeQ[n], n, If[n == 1, 1, n/FactorInteger[n][[1, 1]]]], {n, 1, 76}]
Table[Which[n==1,1,PrimeQ[n],1,True,Divisors[n][[-2]]],{n,80}] (* Harvey P. Dale, Feb 02 2022 *)

Python

import sympy
def A117818(n):
    if n == 1:
        return 1
    else:
        =sympy.ntheory.factor.primefactors(n)
        return _[-1]
print([A117818(n) for n in range(1,100)])
# R. J. Mathar, May 24 2024

Extensions

Edited by Stefan Steinerberger, Jul 22 2007

Extended by Charles R Greathouse IV, Jul 28 2010