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A333849
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a(n) = gcd(A333848(n), 2*(2*n+1)), for n >= 0.
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3
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2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 6, 1, 2, 1, 2, 1, 2, 2, 2, 6, 2, 1, 2, 1, 1, 2, 2, 10, 6, 1, 2, 6, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 6, 2, 2, 2, 2, 1, 6, 1, 2, 6, 2, 2, 6, 2, 1, 2, 2, 1, 6, 1, 2, 2, 2, 1, 2, 2, 2, 6, 2, 1, 2, 10, 2, 2, 2, 1, 10, 1, 2, 18, 2, 2, 2, 1, 2
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OFFSET
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0,1
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COMMENTS
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For n >= 1, a(n) enters the formula for the length L(2*n+1) = A332441(n) of the directed Euler tour ET(2*n+1, q0 = 1) based on the unsigned Schick sequence for 2*n+1, namely L(2*n+1) = A003558(n)*2*(2*n+1)/a(n). For Schick sequences and references see A332439.
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LINKS
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FORMULA
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a(n) = gcd(A333848(n), 2*(2*n+1)), for n >= 0.
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MATHEMATICA
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{2}~Join~Table[GCD[Total@ Select[Range[1, m, 2], GCD[#, m] == 1 &], 2 m], {m, Array[2 # + 1 &, 85]}] (* Michael De Vlieger, Oct 15 2020 *)
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PROG
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(PARI) f(n) = if (n==0, 0, my(m=2*n+1); vecsum(select(x->((gcd(m, x)==1) && (x%2)), [1..m]))); \\ A333848
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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