A106409 n XOR (greatest proper divisor of n).

0, 3, 2, 6, 4, 5, 6, 12, 10, 15, 10, 10, 12, 9, 10, 24, 16, 27, 18, 30, 18, 29, 22, 20, 28, 23, 18, 18, 28, 17, 30, 48, 42, 51, 36, 54, 36, 53, 42, 60, 40, 63, 42, 58, 34, 57, 46, 40, 54, 43, 34, 46, 52, 45, 60, 36, 42, 39, 58, 34, 60, 33, 42, 96, 76, 99, 66, 102, 82, 101, 70

Offset: 1

Author

Reinhard Zumkeller, May 02 2005

Keywords

• nonn
• look

Comments

a(n) = n XOR A032742(n);

a(A000040(n)) = A000040(n) - 1 for n>1;

a(2*n) = A048724(n);

a(A022340(n)) = A022340(n) + A032742(A022340(n)).

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16383

Programs

Maple

a:= n-> Bits[Xor](n, max(1, (numtheory[divisors](n) minus {n})[])):
seq(a(n), n=1..100);  # Alois P. Heinz, May 15 2016

Mathematica

a[1] = 0; a[n_] := BitXor[n, Divisors[n][[-2]]]; Array[a, 100] (* Jean-François Alcover, Mar 12 2019 *)

PARI

gpd(n) = if(n==1, 1, n/factor(n)[1, 1]); \\ A032742
a(n) = bitxor(n, gpd(n)); \\ Michel Marcus, Mar 12 2019