cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A140798 Harmonic numbers that are not multiply-perfect.

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%I A140798 #14 Nov 13 2017 13:20:39
%S A140798 140,270,1638,2970,6200,8190,18600,18620,27846,55860,105664,117800,
%T A140798 167400,173600,237510,242060,332640,360360,539400,695520,726180,
%U A140798 753480,950976,1089270,1421280,1539720,2229500,2290260,2457000,2845800,4358600
%N A140798 Harmonic numbers that are not multiply-perfect.
%C A140798 Sequence is A001599 excluding those entries that appear in A007691.
%C A140798 Multiply-perfect numbers m (with sigma(m)/m an integer) are necessarily harmonic numbers (with tau(m)/{sigma(m)/m } an integer), but the converse is not true : If m divides sigma(m), then quotient sigma(m)/m divides tau(m) [m=A007691]; However, quotient tau(n)/{sigma(n)/n} being an integer does not imply quotient sigma(n)/n is necessarily an integer [n=A001599].
%D A140798 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 140, pp 48, Ellipses, Paris 2008.
%H A140798 Donovan Johnson, <a href="/A140798/b140798.txt">Table of n, a(n) for n = 1..912</a> (terms < 10^14)
%t A140798 Select[Range[10^6], (d = Divisors[#]; IntegerQ[HarmonicMean[d]] && Mod[Total[d], #] != 0)&] (* _Jean-François Alcover_, Nov 13 2017 *)
%Y A140798 Cf. A000203, A054030, A000005.
%K A140798 nonn
%O A140798 1,1
%A A140798 _Lekraj Beedassy_, Jul 15 2008
%E A140798 Initial term 1 removed and offset corrected by _Donovan Johnson_, Jan 25 2012