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Search: id:A003601
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| A003601 |
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Numbers n such that the average of the divisors of n is an integer: sigma_0(n) divides sigma_1(n).
(Formerly M2389)
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+0
23
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| 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102, 103, 105
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sometimes called arithmetic numbers.
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REFERENCES
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R. K. Guy, Unsolved Problems in Number Theory, B2.
Handbook of Number Theory, D. S. Mitrinovic et al., Kluwer, Section III.51.
O. Ore, On the averages of the divisors of a number, Amer. Math. Monthly, 55 (1948), 615-619.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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MAPLE
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with(numtheory); t := [ ]: f := [ ]: for n from 1 to 500 do if sigma(n) mod sigma[ 0 ](n) = 0 then t := [ op(t), n ] else f := [ op(f), n ]; fi; od: t;
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MATHEMATICA
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Select[Range[120], IntegerQ[DivisorSigma[1, # ]/DivisorSigma[0, # ]] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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CROSSREFS
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Complement is A049642. Cf. A000005, A000203, A054025.
Adjacent sequences: A003598 A003599 A003600 this_sequence A003602 A003603 A003604
Sequence in context: A092559 A064728 A046839 this_sequence A072600 A047582 A015814
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas, Mira Bernstein
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EXTENSIONS
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David W. Wilson (davidwwilson(AT)comcast.net) points out that 30 was missing (10/96).
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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