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A163822
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Number of divisors d of 2n such that gcd(d-1,2n/d-1) = 1.
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2
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2, 1, 2, 2, 2, 4, 2, 2, 4, 4, 2, 6, 2, 2, 6, 4, 2, 6, 2, 4, 6, 4, 2, 8, 4, 2, 6, 6, 2, 10, 2, 2, 4, 4, 4, 10, 2, 2, 6, 8, 2, 10, 2, 4, 10, 4, 2, 8, 4, 4, 6, 6, 2, 10, 6, 4, 6, 4, 2, 12, 2, 2, 8, 6, 4, 10, 2, 4, 6, 10, 2, 12, 2, 2, 10, 6, 4, 8, 2, 6, 8, 4, 2, 14, 6, 2, 6, 4, 2, 16, 6, 4, 4, 4, 4, 12, 2, 2, 10
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OFFSET
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1,1
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COMMENTS
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The corresponding values for odd n are all zero, since then 2 is a common divisor of (d-1,n/d-1).
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LINKS
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MATHEMATICA
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a[n_] := DivisorSum[2*n, 1 &, CoprimeQ[#-1, 2*n/#-1] &]; Array[a, 100] (* Amiram Eldar, Apr 23 2024 *)
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PROG
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(PARI) a(n)=local(d, r); r=0; d=divisors(2*n); for(k=1, #d, if(gcd(d[k]-1, 2*n\d[k]-1)==1, r++)); r
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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