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

1,2

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

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 *)

Prog

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

Crossrefs

Sequence in context: A033940 A286367 A196047 * A115510 A230598 A245446

Adjacent sequences: A106406 A106407 A106408 * A106410 A106411 A106412

Keyword

nonn,look

Author

Reinhard Zumkeller, May 02 2005

Status

approved