A285707 a(n) = gcd(n, A079277(n)), a(1) = 1.

1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 3, 8, 1, 2, 1, 4, 3, 2, 1, 6, 5, 2, 9, 4, 1, 3, 1, 16, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 12, 7, 10, 3, 4, 1, 6, 5, 7, 3, 2, 1, 6, 1, 2, 7, 32, 5, 2, 1, 4, 3, 2, 1, 8, 1, 2, 15, 4, 7, 6, 1, 16, 27, 2, 1, 3, 5, 2, 3, 8, 1, 9, 7, 4, 3, 2, 5, 3, 1, 2, 9, 20, 1, 6, 1, 8, 3, 2, 1, 12, 1, 10, 3, 14, 1, 6, 5, 4, 9

Offset: 1

Author

Antti Karttunen, Apr 26 2017

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A009195, A079277, A285699, A285708, A285711.

Programs

Mathematica

Table[GCD[n, #] &@ If[n <= 2, 1, Module[{k = n - 2, e = Floor@ Log2@ n}, While[PowerMod[n, e, k] != 0, k--]; k]], {n, 117}] (* Michael De Vlieger, Apr 26 2017 *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
A079277(n) = { my(r); if((n > 1 && !bitand(n,(n-1))), (n/2), r=A007947(n); if(1==n,0,k = n-1; while(A007947(k*n) <> r, k = k-1); k)); };
A285707(n) = if(1==n,n,gcd(A079277(n),n));

Python

from sympy import divisors, gcd
from sympy.ntheory.factor_ import core
def a007947(n):
    return max(i for i in divisors(n) if core(i) == i)
def a079277(n):
    k=n - 1
    while True:
        if a007947(k*n) == a007947(n): return k
        else: k-=1
def a(n): return 1 if n==1 else gcd(n, a079277(n))
print([a(n) for n in range(1, 151)]) # Indranil Ghosh, Apr 26 2017

Scheme

(define (A285707 n) (if (= 1 n) n (gcd n (A079277 n))))

Formula

a(1) = 1; for n > 1, a(n) = gcd(n, A079277(n)) = gcd(n, A285699(n)).

a(n) = n / A285708(n).