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A094758
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Least k <= n such that n*tau(k) = k*tau(n), where tau(n) is the number of divisors of n (A000005).
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4
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1, 1, 3, 4, 5, 3, 7, 8, 9, 5, 11, 8, 13, 7, 15, 16, 17, 9, 19, 20, 21, 11, 23, 9, 25, 13, 27, 28, 29, 15, 31, 32, 33, 17, 35, 36, 37, 19, 39, 40, 41, 21, 43, 44, 45, 23, 47, 48, 49, 25, 51, 52, 53, 27, 55, 56, 57, 29, 59, 40, 61, 31, 63, 64, 65, 33, 67, 68, 69, 35, 71, 72, 73, 37
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OFFSET
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1,3
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LINKS
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EXAMPLE
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6*tau(3) = 6*2 = 3*4 = 3*tau(6), hence a(6) = 3.
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MAPLE
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for k from 1 to n do
if n*numtheory[tau](k) = k*numtheory[tau](n) then
return k;
end if;
end do:
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MATHEMATICA
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a[n_] := Module[{k = 1, r = DivisorSigma[0, n]/n}, While[DivisorSigma[0, k]/k != r, k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 19 2019 *)
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PROG
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(PARI) for(n=1, 75, s=numdiv(n); k=1; while(n*numdiv(k)!=k*s, k++); print1(k, ", "));
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CROSSREFS
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Cf. A095300 for n such that a(n) < n.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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