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A293212
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Binary XOR of prime divisors of n.
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1
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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
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OFFSET
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2,1
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COMMENTS
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The sequence of indices of zeros begins: 70, 140, 280, 350, 490, 560, 646, 700, 980, 1120, 1292, 1400, 1750, 1798, 1960, 2145.
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LINKS
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FORMULA
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a(n)=n iff n is a prime.
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EXAMPLE
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a(6) = a(24) = 2 XOR 3 = 1.
a(2145) = 3 XOR 5 XOR 11 XOR 13 = 0.
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MAPLE
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a:= proc(n) local d, r; r:=0; for d in numtheory
[factorset](n) do r:= Bits[Xor](r, d) od; r
end:
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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