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A134716 a(n) = least number m such that sigma(m)/m > n, where sigma(m) = sum of divisors of m.

%I A134716 #23 Aug 26 2025 04:58:53
%S A134716 1,2,12,180,27720,122522400,130429015516800,1970992304700453905270400,
%T A134716 1897544233056092162003806758651798777216000,
%U A134716 4368924363354820808981210203132513655327781713900627249499856876120704000
%N A134716 a(n) = least number m such that sigma(m)/m > n, where sigma(m) = sum of divisors of m.
%C A134716 More terms can be obtained by expanding the expressions in the example lines. - _N. J. A. Sloane_, Feb 26 2008
%H A134716 Amiram Eldar, <a href="/A134716/b134716.txt">Table of n, a(n) for n = 0..13</a>
%e A134716 Values written as products of primorials:
%e A134716    n a(n)
%e A134716    0 1
%e A134716    1 2
%e A134716    2 2*3#
%e A134716    3 3#*5# (= 180)
%e A134716    4 2*3#*11#
%e A134716    5 8*5#*17#
%e A134716    6 16*3#*7#*29#
%e A134716    7 8*3#*3#*7#*53#
%e A134716    8 32*3#*3#*5#*11#*89#
%e A134716    9 32*3#*3#*7#*17#*157#
%e A134716   10 16*3#*3#*5#*7#*23#*271#
%e A134716   11 16*3#*3#*5#*7#*29#*487#
%e A134716   12 16*3#*3#*5#*7#*13#*31#*857#
%Y A134716 Cf. A000203 (sigma), A023199 (least k with sigma(k) >= nk).
%K A134716 nonn,changed
%O A134716 0,2
%A A134716 _Pierre CAMI_, Jan 27 2008, corrected Feb 26 2008 with the help of _Emeric Deutsch_