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Search: id:A046999
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| A046999 |
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Non-integer average divisor divides the number. |
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+0
2
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| 28, 496, 8128, 950976, 2178540, 33550336, 142990848, 301953024, 459818240, 675347400, 714954240, 995248800, 1379454720, 2701389600, 3288789504, 6720569856, 8589869056, 10200236032, 14254365440, 30600708096, 42763096320, 43861478400, 66433720320, 71271827200
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The sequence contains perfect numbers (A000396) and others. Most of them have only small prime factors.
The first three terms are in A007691 (multiply perfect numbers) but 950976 is not since Sigma_1/x is not an integer.
sigma_0(n) is the number of divisors of n (A000005).
sigma_1(n) is the sum of the divisors of n [same as sigma(n)] (A000203).
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FORMULA
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Average divisor=a=Sigma_1(x)/Sigma_0(x) is not an integer but x/a is.
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EXAMPLE
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x=28, Sigma_0=6, Sigma_1=56, a=S1/S0=9.33 is not an integer but x/a=3 is; x=950976, a=2958592/84=3521.33 but x/a=27 is integral.
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CROSSREFS
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In A001599 but not in A003601. Cf. A007691, A046985 - A046987, A000396.
Sequence in context: A076172 A004336 A079598 this_sequence A046986 A028145 A028167
Adjacent sequences: A046996 A046997 A046998 this_sequence A047000 A047001 A047002
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
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More terms from Jud McCranie (j.mccranie(AT)comcast.net), Dec 25 2000
a(16)-a(24) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Apr 22 2008
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