A046061 6-multiperfect numbers.

154345556085770649600, 9186050031556349952000, 680489641226538823680000, 6205958672455589512937472000, 13297004660164711617331200000, 15229814702070563916152832000

Offset

1,1

Comments

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

Links

T. D. Noe, Table of n, a(n) for n = 1..245 (complete sequence from Flammenkamp)

F. Firoozbakht, M. F. Hasler, Variations on Euclid's formula for Perfect Numbers, JIS 13 (2010) #10.3.1.

Achim Flammenkamp, The Multiply Perfect Numbers Page

Fred Helenius, Link to Glossary and Lists

Walter Nissen, Abundancy : Some Resources

Eric Weisstein's World of Mathematics, Multiperfect Number.

Example

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)

Prog

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

Crossrefs

Cf. A000396, A005820, A027687, A046060, A007539.

Sequence in context: A290156 A095436 A247262 * A181790 A252504 A338983

Adjacent sequences: A046058 A046059 A046060 * A046062 A046063 A046064

Keyword

nonn

Author

Eric W. Weisstein

Status

approved