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A234520 Composite numbers n sorted by decreasing values of beta(n) = sigma(n)^(1/n) - (n+1)^(1/n), where sigma(n) = A000203(n) = the sum of divisors of n. 12
4, 6, 8, 12, 10, 18, 16, 24, 14, 20, 9, 15, 30, 36, 28, 22, 32, 40, 48, 42, 21, 26, 60, 54, 44, 27, 72, 56, 34, 50, 45, 52, 38, 66, 84, 33, 64, 90, 80, 70, 96, 78, 46, 39, 120, 68, 108, 35, 88, 76, 63, 25, 100, 58, 102, 126, 144, 112, 132, 62, 104, 75, 51, 92 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The number beta(n) = sigma(n)^(1/n) - (n+1)^(1/n) is called the beta-deviation from primality of the number n; beta(p) = 0 for p = prime. See A234516 for definition of alpha(n).
For number 4; beta(4) = sigma(4)^(1/4) - (4+1)^(1/4), = 7^(1/4) - 5^(1/4) = 0,131227780… = A234522 (maximal value of function beta(n)).
Lim_n->infinity beta(n) = 0.
Conjecture: Every composite number n has a unique value of number beta(n).
See A234523 - sequence of numbers a(n) such that a(n) > a(k) for all k < n.
LINKS
CROSSREFS
Sequence in context: A352374 A110646 A320126 * A275789 A031359 A274790
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 14 2014
STATUS
approved

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Last modified July 21 20:59 EDT 2024. Contains 374475 sequences. (Running on oeis4.)