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A005820 Triply perfect (tri-perfect, or triperfect) numbers: sum of divisors of n is 3n.
(Formerly M5376)
+0
16
120, 672, 523776, 459818240, 1476304896, 51001180160 (list; graph; listen)
OFFSET

1,1

REFERENCES

A. Brousseau, Number Theory Tables. Fibonacci Association, San Jose, CA, 1973, p. 138.

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 120, p. 42, Ellipses, Paris 2008.

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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Stewart, L'univers des nombres, "Les nombres multiparfaits", Chap.15, pp 82-5, Belin/Pour la Science, Paris 2000.

David Wells, "The Penguin Book of Curious and Interesting Numbers," Penguin Books, London, 1986, pages 135, 159 and 185.

LINKS

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, Link to a section of The World of Mathematics (1).

Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).

EXAMPLE

sigma(120)=360=3*120

MATHEMATICA

AbundantQ[n_]:=DivisorSigma[1, n]==3*n; a={}; Do[If[AbundantQ[n], AppendTo[a, n]], {n, 10^6}]; a [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 07 2008]

CROSSREFS

Cf. A007539, A000396, A027687, A046060, A046061.

Sequence in context: A114887 A069085 A039688 this_sequence A052787 A052769 A052766

Adjacent sequences: A005817 A005818 A005819 this_sequence A005821 A005822 A005823

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

Wells gives the 6th term as 31001180160, but this is an error.

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Last modified December 15 00:47 EST 2009. Contains 170825 sequences.


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