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A046060 5-multiperfect numbers.

%I A046060 #39 Jul 18 2025 11:07:52
%S A046060 14182439040,31998395520,518666803200,13661860101120,30823866178560,
%T A046060 740344994887680,796928461056000,212517062615531520,
%U A046060 69357059049509038080,87934476737668055040,170206605192656148480,1161492388333469337600,1245087725796543283200,1802582780370364661760
%N A046060 5-multiperfect numbers.
%C A046060 Conjectured finite and probably these are the only terms; cf. Flammenkamp's link. [_Georgi Guninski_, Jul 25 2012]
%D A046060 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 143.
%H A046060 T. D. Noe, <a href="/A046060/b046060.txt">Table of n, a(n) for n = 1..65</a> (complete sequence from Flammenkamp)
%H A046060 Farideh Firoozbakht and 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 A046060 Achim Flammenkamp, <a href="http://wwwhomes.uni-bielefeld.de/achim/mpn.html">The Multiply Perfect Numbers Page</a>.
%H A046060 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 A046060 Fred Helenius, <a href="http://pw1.netcom.com/~fredh/index.html">Link to Glossary and Lists</a>.
%H A046060 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">Abundancy : Some Resources </a>.
%H A046060 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MultiperfectNumber.html">Multiperfect Number</a>.
%e A046060 From _Daniel Forgues_, May 09 2010: (Start)
%e A046060 14182439040 = 2^7*3^4*5*7*11^2*17*19
%e A046060 sigma(14182439040)
%e A046060   = (2^8-1)/1*(3^5-1)/2*(5^2-1)/4*(7^2-1)/6*(11^3-1)/10*(17^2-1)/16*(19^2-1)/18
%e A046060   = (255)*(121)*(6)*(8)*(133)*(18)*(20)
%e A046060   = (3*5*17)*(11^2)*(2*3)*(2^3)*(7*19)*(2*3^2)*(2^2*5)
%e A046060   = 2^7*3^4*5^2*7*11^2*17*19
%e A046060   = (5) * (2^7*3^4*5*7*11^2*17*19)
%e A046060   = 5 * 14182439040 (End)
%o A046060 (PARI) is(n)=sigma(n)==5*n \\ _Charles R Greathouse IV_, Apr 05 2013
%Y A046060 Cf. A000396, A005820, A027687, A046061, A007539.
%K A046060 nonn
%O A046060 1,1
%A A046060 _Eric W. Weisstein_