

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 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

Jaroslav Krizek, Table of n, a(n) for n = 1..1000


CROSSREFS

Cf. A234515, A234516, A234517, A234518, A234519, A234521, A234522, A234523, A234524.
Sequence in context: A320127 A110646 A320126 * A275789 A031359 A274790
Adjacent sequences: A234517 A234518 A234519 * A234521 A234522 A234523


KEYWORD

nonn


AUTHOR

Jaroslav Krizek, Jan 14 2014


STATUS

approved



