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A046061 6-multiperfect numbers.

%I A046061 #42 Jul 18 2025 10:33:02
%S A046061 154345556085770649600,9186050031556349952000,
%T A046061 680489641226538823680000,6205958672455589512937472000,
%U A046061 13297004660164711617331200000,15229814702070563916152832000
%N A046061 6-multiperfect numbers.
%C A046061 Conjectured finite and probably these are the only terms; cf. Flammenkamp's link. - _Georgi Guninski_, Jul 25 2012
%D A046061 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 144.
%H A046061 T. D. Noe, <a href="/A046061/b046061.txt">Table of n, a(n) for n = 1..245</a> (complete sequence from Flammenkamp)
%H A046061 Farideh Firoozbakht, Maximilian F. Hasler, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Hasler/hasler2.html">Variations on Euclid's formula for Perfect Numbers</a>, JIS 13 (2010) #10.3.1.
%H A046061 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>
%H A046061 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_6">Perfect, Multiply Perfect, and Sociable Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 6, 185-207.
%H A046061 Fred Helenius, <a href="http://pw1.netcom.com/~fredh/index.html">Link to Glossary and Lists</a>
%H A046061 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources </a>
%H A046061 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number.</a>
%e A046061 From _Daniel Forgues_, May 09 2010: (Start)
%e A046061 154345556085770649600 = 2^15*3^5*5^2*7^2*11*13*17*19*31*43*257
%e A046061 sigma(154345556085770649600) =
%e A046061 (2^16-1)/1*(3^6-1)/2*(5^3-1)/4*(7^3-1)/6*(11^2-1)/10*(13^2-1)/12*(17^2-1)/16*(19^2-1)/18*(31^2-1)/30*(43^2-1)/42*(257^2-1)/256
%e A046061 = 65535*364*31*57*12*14*18*20*32*44*258
%e A046061 = (5*3*17*257)*(2^2*7*13)*(31)*(3*19)*(2^2*3)*(2*7)*(2*3^2)*(2^2*5)*(2^5)*(2^2*11)*(2*3*43)
%e A046061 = 2^16*3^6*5^2*7^2*11*13*17*19*31*43*257
%e A046061 = (2*3) * (2^15*3^5*5^2*7^2*11*13*17*19*31*43*257)
%e A046061 = 6 * 154345556085770649600 (End)
%o A046061 (PARI) is(n)=sigma(n)==6*n \\ _Charles R Greathouse IV_, Apr 05 2013
%Y A046061 Cf. A000396, A005820, A027687, A046060, A007539.
%K A046061 nonn
%O A046061 1,1
%A A046061 _Eric W. Weisstein_