A046061 6-multiperfect numbers.

154345556085770649600, 9186050031556349952000, 680489641226538823680000, 6205958672455589512937472000, 13297004660164711617331200000, 15229814702070563916152832000

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)
154345556085770649600 = 2^15*3^5*5^2*7^2*11*13*17*19*31*43*257
sigma(154345556085770649600) =
(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
= 65535*364*31*57*12*14*18*20*32*44*258
= (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)
= 2^16*3^6*5^2*7^2*11*13*17*19*31*43*257
= (2*3) * (2^15*3^5*5^2*7^2*11*13*17*19*31*43*257)
= 6 * 154345556085770649600 (End)
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 144.

Links

• T. D. Noe, Table of n, a(n) for n = 1..245 (complete sequence from Flammenkamp)
• Farideh Firoozbakht, 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, A046060, A007539.

Programs

PARI

is(n)=sigma(n)==6*n \\ Charles R Greathouse IV, Apr 05 2013