

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
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OFFSET

1,1


COMMENTS

The number beta(n) = sigma(n)^(1/n)  (n+1)^(1/n) is called the betadeviation 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



KEYWORD

nonn


AUTHOR



STATUS

approved



