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 A268387 Bitwise-XOR of the exponents of primes in the prime factorization of n. 16
 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 FORMULA a(1) = 0; for n > 1: a(n) = A067029(n) XOR a(A028234(n)). [Here XOR stands for bitwise exclusive-or, A003987.] Other identities and observations. For all n >= 1: a(n) <= A267116(n) <= A001222(n). From Peter Munn, Dec 02 2019 with XOR used as above: (Start) Defined by: a(p^k) = k, for prime p; a(A059897(n,k)) = a(n) XOR a(k). a(A052330(n XOR k)) = a(A052330(n)) XOR a(A052330(k)). a(A019565(n XOR k)) = a(A019565(n)) XOR a(A019565(k)). (End) 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 A003987, A028234, A059897 and A067029 are used to express relationships between sequence terms. Cf. A268390 (indices of zeros). Sequences with similar definitions: A267115, A267116. Differs from A136566 for the first time at n=24, where a(24) = 2, while A136566(24) = 4. Cf. A019565, A052330. Sequence in context: A319273 A329615 A272894 * A136566 A330235 A048983 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 April 19 21:57 EDT 2021. Contains 343117 sequences. (Running on oeis4.)