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A007539 First n-fold perfect number.
(Formerly M4297)
16
1, 6, 120, 30240, 14182439040, 154345556085770649600, 141310897947438348259849402738485523264343544818565120000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

On the Riemann Hypothesis, a(n) > exp(exp(n / e^gamma)) for n > 3. Unconditionally, a(n) > exp(exp(0.9976n / e^gamma)) for n > 3, where the constant is related to A004394(1000000). - Charles R Greathouse IV, Sep 06 2012

Each of the terms 1, 6, 120, 30240 divides all larger terms <= a(8). See A227765, A227766, ..., A227769. - Jonathan Sondow, Jul 30 2013

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 22.

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

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).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..8

C. K. Caldwell, The Prime Glossary, multiply perfect

Achim Flammenkamp, The Multiply Perfect Numbers Page

Fred Helenius, Link to Glossary and Lists

Walter Nissen, Abundancy: Some Resources

CROSSREFS

Cf. A000396, A005820, A027687, A046060, A046061, A007691, A072002, A227765, A227766, A227767, A227768, A227769.

Sequence in context: A012475 A053777 A023199 * A040996 A110442 A137149

Adjacent sequences:  A007536 A007537 A007538 * A007540 A007541 A007542

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms sent by Robert G. Wilson v, Nov 30 2000

STATUS

approved

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Last modified December 22 00:23 EST 2014. Contains 252326 sequences.