Search: id:A007340 Results 1-1 of 1 results found. %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, Factorizations of many number sequences %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. Search completed in 0.001 seconds