A046060 5-multiperfect numbers.

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

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..65 (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)
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)

Prog

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

Crossrefs

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

Sequence in context: A017616 A304234 A134298 * A172595 A172617 A216015

Adjacent sequences: A046057 A046058 A046059 * A046061 A046062 A046063

Keyword

nonn

Author

Eric W. Weisstein

Status

approved