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A027687 4-perfect (quadruply-perfect or sous-triple) numbers: sum of divisors of n is 4n. 20
30240, 32760, 2178540, 23569920, 45532800, 142990848, 1379454720, 43861478400, 66433720320, 153003540480, 403031236608, 704575228896, 181742883469056, 6088728021160320, 14942123276641920, 20158185857531904, 275502900594021408 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

It is conjectured that there are only finitely many terms. - N. J. A. Sloane, Jul 22 2012

Odd perfect number (unlikely to exist) and infinitely many Mersenne primes will make the sequence infinite - take the product of the OPN and coprime EPNs.

Conjecture: A010888(a(n)) divides a(n). Tested for n up to 36 incl. - Ivan N. Ianakiev, Oct 31 2013

REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, B2.

LINKS

T. D. Noe, Table of n, a(n) for n=1..36 (complete sequence from Flammenkamp)

Walter Nissen, Abundancy : Some Resources

Achim Flammenkamp, The Multiply Perfect Numbers Page

Fred Helenius, Link to Glossary and Lists

Eric Weisstein's World of Mathematics, Multiperfect Number.

Eric Weisstein's World of Mathematics, Sous-Triple.

Wikipedia, Multiply perfect number

EXAMPLE

Contribution from Daniel Forgues, May 09 2010: (Start)

30240 = 2^5*3^3*5*7

sigma(30240) = (2^6-1)/1*(3^4-1)/2*(5^2-1)/4*(7^2-1)/6

= (63)*(40)*(6)*(8)

= (7*3^2)*(2^3*5)*(2*3)*(2^3)

= 2^7*3^3*5*7

= (2^2) * (2^5*3^3*5*7)

= 4 * 30240 (End)

MATHEMATICA

AbundantQ[n_]:=DivisorSigma[1, n]==4*n; a={}; Do[If[AbundantQ[n], AppendTo[a, n]], {n, 10^6}]; a [From Vladimir Joseph Stephan Orlovsky, Aug 16 2008]

CROSSREFS

Cf. A007539, A000396, A005820, A046060, A046061.

Sequence in context: A027665 A202598 A113286 * A190475 A218029 A109485

Adjacent sequences:  A027684 A027685 A027686 * A027688 A027689 A027690

KEYWORD

nonn

AUTHOR

Jean-Yves Perrier (nperrj(AT)ascom.ch)

EXTENSIONS

4 more terms from Labos Elemer

STATUS

approved

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Last modified April 24 19:08 EDT 2014. Contains 240988 sequences.