%I A007340 M4299
%S A007340 1,6,140,270,672,1638,2970,6200,8190,18600,18620,27846,30240,32760,55860,
               105664,
%T A007340 117800,167400,173600,237510,242060,332640,360360,539400,695520,726180,
               753480,
%U A007340 1089270,1421280,1539720,2229500,2290260,2457000
%N A007340 Numbers n such that both the harmonic and arithmetic means of the divisors 
               of n are integers.
%C A007340 Intersection of A001599 and A003601.
%C A007340 The following are also in A046985: 1,6,672,30240,32760. Also contains 
               multiply perfect (A007691) numbers. - Labos E. (labos(AT)ana.sote.hu)
%D A007340 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007340 G. L. Cohen, personal communication.
%D A007340 T. Goto and S. Shibata, All numbers whose positive divisors have integral 
               harmonic mean up to 300, Math. Comput. 73 (2004), 475-491.
%D A007340 R. K. Guy, Unsolved Problems in Number Theory, B2.
%D A007340 O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 
               55 (1948), 615-619.
%D A007340 N. J. A. Sloane, Illustration for sequence M4299 (=A007340) in The Encyclopedia 
               of Integer Sequences (with S. Plouffe), Academic Press, 1995.
%D A007340 D. Wells, Curious and interesting numbers, Penguin Books, p. 124.
%H A007340 Hisanori Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/
               matha1/matha138.htm">Factorizations of many number sequences</a>
%F A007340 a=Sigma[ 1, x ]/Sigma[ 0, x ] integer and b=x/a also.
%e A007340 x=270: Sigma[ 0,270 ]=16, Sigma[ 1,270 ]=720; average divisor a=720/16=45 
               and integer 45 divides x, x/a=270/45=6, but 270 is not in A007691.
%t A007340 Do[ a = DivisorSigma[0, n]/ DivisorSigma[1, n]; If[IntegerQ[n*a] && IntegerQ[1/
               a], Print[n]], {n, 1, 2500000}] - Labos E. (labos(AT)ana.sote.hu)
%Y A007340 Intersection of A003601 and A001599. Cf. A007691, A046985 - A046987, 
               A046999.
%Y A007340 Different from A090945.
%Y A007340 Sequence in context: A155558 A053467 A090944 this_sequence A122483 A123729 
               A123728
%Y A007340 Adjacent sequences: A007337 A007338 A007339 this_sequence A007341 A007342 
               A007343
%K A007340 nonn,nice
%O A007340 1,2
%A A007340 N. J. A. Sloane (njas(AT)research.att.com).
%E A007340 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 03 2002
%E A007340 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 05 2008 at 
               the suggestion of R. J. Mathar.