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A236022
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Composite numbers n sorted by increasing values of gamma(n) = log_2(n+1) - log_tau(n) (sigma(n)), where sigma(n) = A000203(n) = the sum of divisors of n and tau(n) = A000005(n) = the number of divisors of n.
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8
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4, 9, 6, 8, 10, 25, 14, 15, 12, 22, 16, 21, 49, 26, 27, 18, 34, 33, 20, 38, 35, 39, 46, 121, 28, 51, 58, 169, 24, 62, 57, 55, 32, 74, 69, 65, 82, 30, 86, 289, 94, 77, 87, 44, 85, 93, 106, 361, 45, 91, 95, 50, 118, 36, 52, 122, 111, 40, 42, 134, 123, 115, 142
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OFFSET
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1,1
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COMMENTS
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The number gamma(n) = log_2(n+1) - log_tau(n) (sigma(n)) is called the gamma-deviation from primality of the number n; gamma(p) = 0 for p = prime.
Conjecture: every natural number n has a unique value of gamma(n).
For number 4; gamma(4) = log_2 (4+1) - log_tau(4) (sigma(4)) = log_2 (5) - log_3 (7) = 0,5506843457… = A236023 (minimal value of function gamma(n)).
See A236024 - sequence of numbers from a(n) such that a(n) > a(k) for all k < n.
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LINKS
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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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