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
Jaroslav Krizek, Table of n, a(n) for n = 1..1000
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Jan 14 2014
STATUS
approved