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A268387 Bitwise-XOR of the exponents of primes in the prime factorization of n. 12
0, 1, 1, 2, 1, 0, 1, 3, 2, 0, 1, 3, 1, 0, 0, 4, 1, 3, 1, 3, 0, 0, 1, 2, 2, 0, 3, 3, 1, 1, 1, 5, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 1, 3, 3, 0, 1, 5, 2, 3, 0, 3, 1, 2, 0, 2, 0, 0, 1, 2, 1, 0, 3, 6, 0, 1, 1, 3, 0, 1, 1, 1, 1, 0, 3, 3, 0, 1, 1, 5, 4, 0, 1, 2, 0, 0, 0, 2, 1, 2, 0, 3, 0, 0, 0, 4, 1, 3, 3, 0, 1, 1, 1, 2, 1, 0, 1, 1, 1, 1, 0, 5, 1, 1, 0, 3, 3, 0, 0, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(1) = 0; for n > 1: a(n) = A067029(n) XOR a(A028234(n)). [Here XOR stands for bitwise-or, A003987.]

Other identities and observations. For all n >= 1:

a(n) <= A267116(n) <= A001222(n).

MATHEMATICA

Table[BitXor @@ Map[Last, FactorInteger@ n], {n, 120}] (* Michael De Vlieger, Feb 12 2016 *)

PROG

(Scheme, with memoization-macro definec)

(definec (A268387 n) (cond ((= 1 n) 0) (else (A003987bi (A067029 n) (A268387 (A028234 n)))))) ;; A003987bi implements bitwise-xor (see A003987).

(PARI) a(n) = {my(f = factor(n)); my(b = 0); for (k=1, #f~, b = bitxor(b, f[k, 2]); ); b; } \\ Michel Marcus, Feb 06 2016

CROSSREFS

Cf. A003987, A028234, A067029.

Cf. A268390 (indices of zeros).

Cf. also A267115, A267116.

Differs from A136566 for the first time at n=24, where a(24) = 2, while A136566(24) = 4.

Sequence in context: A255740 A100995 A272894 * A136566 A048983 A256140

Adjacent sequences:  A268384 A268385 A268386 * A268388 A268389 A268390

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Feb 05 2016

STATUS

approved

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Last modified December 11 21:15 EST 2017. Contains 295919 sequences.