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A343945
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a(1) = 1; for n >= 2, a(n) = floor(log(sigma(n)) / log(tau(n))).
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0
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1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 3, 2, 2, 2, 4, 2, 4, 2, 2, 2, 4, 1, 3, 2, 2, 2, 4, 2, 5, 2, 2, 2, 2, 2, 5, 2, 2, 2, 5, 2, 5, 2, 2, 3, 5, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 3, 5, 2, 5, 3, 2, 2, 3, 2, 6, 2, 3, 2, 6, 2, 6, 3, 2, 2, 3, 2, 6, 2, 2, 3, 6, 2, 3, 3, 3
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OFFSET
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1,3
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COMMENTS
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See A051281 for numbers m such that sigma(m) = tau(m)^k where k = integer, i.e., numbers m such that floor(log(sigma(m)) / log(tau(m))) = log(sigma(m)) / log(tau(m)).
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LINKS
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EXAMPLE
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a(6) = floor(log(sigma(6)) / log(tau(6))) = floor(log(12) / log(4)) = floor(1.792481...) = 1.
a(7) = floor(log(sigma(7)) / log(tau(7))) = floor(log(8) / log(2)) = floor(3) = 3.
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MATHEMATICA
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a[1] = 1; a[n_] := Floor[Log @@ DivisorSigma[{0, 1}, n]]; Array[a, 100] (* Amiram Eldar, Dec 16 2021 *)
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PROG
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(Magma) [1] cat [Floor(Log(&+Divisors(n)) / Log(#Divisors(n))): n in [2..100]]
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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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