A046060 5-multiperfect numbers.

14182439040, 31998395520, 518666803200, 13661860101120, 30823866178560, 740344994887680, 796928461056000, 212517062615531520, 69357059049509038080, 87934476737668055040, 170206605192656148480, 1161492388333469337600, 1245087725796543283200, 1802582780370364661760

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Conjectured finite and probably these are the only terms; cf. Flammenkamp's link. [Georgi Guninski, Jul 25 2012]

Examples

			From _Daniel Forgues_, May 09 2010: (Start)
14182439040 = 2^7*3^4*5*7*11^2*17*19
sigma(14182439040)
  = (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
  = (255)*(121)*(6)*(8)*(133)*(18)*(20)
  = (3*5*17)*(11^2)*(2*3)*(2^3)*(7*19)*(2*3^2)*(2^2*5)
  = 2^7*3^4*5^2*7*11^2*17*19
  = (5) * (2^7*3^4*5*7*11^2*17*19)
  = 5 * 14182439040 (End)
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 143.

Links

• T. D. Noe, Table of n, a(n) for n = 1..65 (complete sequence from Flammenkamp)
• Farideh Firoozbakht and Maximilian F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.
• Achim Flammenkamp, The Multiply Perfect Numbers Page.
• Shyam Sunder Gupta, Perfect, Multiply Perfect, and Sociable Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 6, 185-207.
• Fred Helenius, Link to Glossary and Lists.
• Walter Nissen, Abundancy : Some Resources .
• Eric Weisstein's World of Mathematics, Multiperfect Number.

Crossrefs

Cf. A000396, A005820, A027687, A046061, A007539.

Programs

PARI

is(n)=sigma(n)==5*n \\ Charles R Greathouse IV, Apr 05 2013