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A240667
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a(n) is the GCD of the solutions x of sigma(x) = n; sigma(n) = A000203(n) = sum of divisors of n.
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8
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1, 0, 2, 3, 0, 5, 4, 7, 0, 0, 0, 1, 9, 13, 8, 0, 0, 1, 0, 19, 0, 0, 0, 1, 0, 0, 0, 12, 0, 29, 1, 1, 0, 0, 0, 22, 0, 37, 18, 27, 0, 1, 0, 43, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 49, 0, 0, 1, 0, 61, 32, 0, 0, 0, 0, 67, 0, 0, 0, 1, 0, 73, 0, 0, 0, 45, 0, 1, 0, 0
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OFFSET
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1,3
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COMMENTS
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From n=1 to 5, the least integers such that a(x)=n, depending on if singletons (see A007370 and A211656) are accepted or not, are 1, 3, 4, 7, 6 or 12, 126, 124, 210, 22152.
Is it possible to find an integer n such that a(n) = 6?
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LINKS
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FORMULA
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EXAMPLE
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There are no integers such that sigma(x)=2, so a(2)=0.
There is a single integer, x=2, such that sigma(x)=3, so a(3)=2.
There are 2 integers, x=6 and 11, such that sigma(x)=12, their gcd is 1, so a(12)=1.
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MAPLE
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A240667 := n -> igcd(op(select(k->sigma(k)=n, [$1..n]))):
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MATHEMATICA
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a[n_] := GCD @@ Select[Range[n], DivisorSigma[1, #] == n&];
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PROG
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(PARI) sigv(n) = select(i->sigma(i) == n, vector(n, i, i));
a(n) = {v = sigv(n); if (#v == 0, 0, gcd(v)); }
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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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