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A068403 Numbers n such that sigma(n) > 3n. 12
180, 240, 360, 420, 480, 504, 540, 600, 660, 720, 780, 840, 900, 960, 1008, 1080, 1200, 1260, 1320, 1344, 1440, 1512, 1560, 1584, 1620, 1680, 1800, 1848, 1872, 1890, 1920, 1980, 2016, 2040, 2100, 2160, 2184, 2280, 2340, 2352, 2376, 2400, 2520, 2640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Davenport shows that these numbers have positive density. Are there good bounds for the density?

G. Miller & M. Whalen suggested that 1018976683725 (3^3*5^2*7^2*11*13*17*19*23*29) might be the smallest odd number in the sequence (a fact now, see A119240 and A023197). - Michel Marcus, May 01 2013

REFERENCES

H. Davenport, Über numeri abundantes, Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl., No. 6 (1933), pp. 830-837.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Gordon L. Miller and Mary T. Whalen, Multiply Abundant Numbers, School Science and Mathematics, Volume 95, Issue 5, pages 256-259, May 1995.

MAPLE

A068403:=n->`if`((numtheory)[sigma](n) > 3*n, n, NULL): seq(A068403(n), n=1..5*10^3); # Wesley Ivan Hurt, Apr 09 2017

MATHEMATICA

Select[Range[180, 7!, 2], 3*# < Plus@@Divisors[ # ]&] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2010 *)

PROG

(PARI) for(n=1, 3000, if(sigma(n)>3*n, print1(n, ", "))) \\ Indranil Ghosh, Apr 10 2017

(Python)

from sympy import divisor_sigma

print [n for n in range(1, 3001) if divisor_sigma(n)>3*n] # Indranil Ghosh, Apr 10 2017

CROSSREFS

Terms not divisible by 6 are in A126104.

Cf. A068404, A215264.

Cf. A005820 (3-perfect numbers).

Sequence in context: A260265 A117551 A068545 * A291457 A329189 A289056

Adjacent sequences:  A068400 A068401 A068402 * A068404 A068405 A068406

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Mar 02 2002

STATUS

approved

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Last modified October 1 12:43 EDT 2020. Contains 337443 sequences. (Running on oeis4.)