%I A011257
%S A011257 1,14,30,51,105,170,194,248,264,364,405,418,477,595,679,714,760,780,1023,
%T A011257 1455,1463,1485,1496,1512,1524,1674,1715,1731,1796,1804,2058,2080,2651,
%U A011257 2754,2945,3080,3135,3192,3410,3534,3567,3596,3828,3956,4064,4381,4420
%N A011257 Geometric mean of phi(n) and sigma(n) is an integer.
%C A011257 For these terms the arithmetic mean is also an integer. It is conjectured 
               that sigma(n) for these numbers is never odd. See also A065146, A028982, 
               A028983. - Labos E. (labos(AT)ana.sote.hu), Oct 18 2001
%C A011257 If p>2 and 2^p-1 is prime (a Mersenne prime) then m=2^(p-2)*(2^p-1) is 
               in the sequence because phi(m)=2^(p-2)*(2^(p-1)-1); sigma(m)= (2^(p-1)-1)*2^p 
               hence (phi(m)*sigma(m))^(1/2)=2^(p-1)*(2^(p-1)-1) is an integer. 
               So for n>1, 2^(A000043(n)-2)*2^(A000043(n)-1) is in the sequence. 
               - Farideh Firoozbakht (mymontain(AT)yahoo.com), Nov 27 2005
%C A011257 From a(2633)=6931232 on, it is no longer true (as was once conjectured) 
               that a(n)>n^2. - M. F. Hasler, Feb 07 2009
%D A011257 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 51, p. 19, Ellipses, 
               Paris 2008.
%D A011257 R. K. Guy, Divisors and desires, Amer. Math. Monthly, 104 (1997), 359-360.
%D A011257 Zhang Ming-Zhi (typescript submitted to Unsolved Problems section of 
               Monthly, 96-01-10)
%H A011257 M. F. Hasler, <a href="b011257.txt">Table of n, a(n) for n=1,...,2000</
               a>
%Y A011257 Cf. A000043, A000668.
%Y A011257 Sequence in context: A044075 A044456 A132759 this_sequence A083540 A027575 
               A104776
%Y A011257 Adjacent sequences: A011254 A011255 A011256 this_sequence A011258 A011259 
               A011260
%K A011257 nonn
%O A011257 1,2
%A A011257 N. J. A. Sloane (njas(AT)research.att.com).