%I #23 Oct 08 2017 13:27:15

%S 120,672,32760,2178540,1379454720,14182439040,518666803200,

%T 30823866178560,71065075104190073088,154345556085770649600,

%U 9186050031556349952000,680489641226538823680000

%N Multiperfect numbers sigma(n) = k*n, which are divisible by the sum of their prime factors without repetition.

%C From a list of about 5000 multiperfect numbers, 38 numbers were found with the property, all having k <= 9, the largest was the only one having k=9. A091443 uses sopfr with repetition.

%C Conjecture: the sequence is finite.

%H Sven Simon, <a href="/A114887/b114887.txt">Table of n, a(n) for n = 1..38</a> [Conjectured to be complete]

%H Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a> (See here for the latest information about the search)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect numbers</a>

%e a(0) = 120 = 2^3*3*5, sopf(120) = 2+3+5 = 10.

%Y Cf. A091443.

%Y Intersection of A007691 and A089352. - _Michel Marcus_, Oct 08 2017

%K nonn

%O 1,1

%A _Sven Simon_, Feb 19 2006