A293212 Binary XOR of prime divisors of n.

2, 3, 2, 5, 1, 7, 2, 3, 7, 11, 1, 13, 5, 6, 2, 17, 1, 19, 7, 4, 9, 23, 1, 5, 15, 3, 5, 29, 4, 31, 2, 8, 19, 2, 1, 37, 17, 14, 7, 41, 6, 43, 9, 6, 21, 47, 1, 7, 7, 18, 15, 53, 1, 14, 5, 16, 31, 59, 4, 61, 29, 4, 2, 8, 10, 67, 19, 20, 0, 71, 1, 73, 39, 6, 17

Offset

2,1

Comments

The sequence of indices of zeros begins: 70, 140, 280, 350, 490, 560, 646, 700, 980, 1120, 1292, 1400, 1750, 1798, 1960, 2145.

Links

Alois P. Heinz, Table of n, a(n) for n = 2..20000

Formula

a(n)=n iff n is a prime.

Example

a(6) = a(24) = 2 XOR 3 = 1.
a(2145) = 3 XOR 5 XOR 11 XOR 13 = 0.

Maple

a:= proc(n) local d, r; r:=0; for d in numtheory
      [factorset](n) do r:= Bits[Xor](r, d) od; r
    end:
seq(a(n), n=2..100);  # Alois P. Heinz, Mar 09 2018

Prog

(PARI) a(n) = my(vp = factor(n)[, 1]~, k=0); for (i=1, #vp, k = bitxor(k, vp[i])); k; \\ Michel Marcus, Feb 05 2018

Crossrefs

Cf. A000040, A072594, A178910.

Sequence in context: A300852 A332881 A332424 * A157449 A053139 A127705

Adjacent sequences: A293209 A293210 A293211 * A293213 A293214 A293215

Keyword

nonn,base

Author

Alex Ratushnyak, Feb 04 2018

Status

approved