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 A268387 Bitwise-XOR of the exponents of primes in the prime factorization of n. 13
 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-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: A100995 A319273 A272894 * A136566 A048983 A301505 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 11:30 EST 2018. Contains 318049 sequences. (Running on oeis4.)