cp's OEIS Frontend

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.

%I A234520 #7 Jan 21 2014 08:10:20
%S A234520 4,6,8,12,10,18,16,24,14,20,9,15,30,36,28,22,32,40,48,42,21,26,60,54,
%T A234520 44,27,72,56,34,50,45,52,38,66,84,33,64,90,80,70,96,78,46,39,120,68,
%U A234520 108,35,88,76,63,25,100,58,102,126,144,112,132,62,104,75,51,92
%N 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.
%C A234520 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).
%C A234520 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)).
%C A234520 Lim_n->infinity beta(n) = 0.
%C A234520 Conjecture: Every composite number n has a unique value of number beta(n).
%C A234520 See A234523 - sequence of numbers a(n) such that a(n) > a(k) for all k < n.
%H A234520 Jaroslav Krizek, <a href="/A234520/b234520.txt">Table of n, a(n) for n = 1..1000</a>
%Y A234520 Cf. A234515, A234516, A234517, A234518, A234519, A234521, A234522, A234523, A234524.
%K A234520 nonn
%O A234520 1,1
%A A234520 _Jaroslav Krizek_, Jan 14 2014