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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). Alternatively, tau(n) (A000005(n)) divides sigma(n) (A000203(n)).
(Formerly M2389)
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+0
34
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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.
Generalized (sigma_r)-numbers are numbers n for which sigma_r(n)/sigma_0(n) = c^r . Sigma_r(n) denotes sum of r-th powers of divisors of n; c,r positive integers. This sequence are sigma_1-numbers, A140480 are sigma_2-numbers. - Ctibor O. Zizka (ctibor.zizka(AT)seznam.cz), Jul 14 2008
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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, A001599, A007340, A140480.
Sequence in context: A092559 A064728 A046839 this_sequence A072600 A047582 A015814
Adjacent sequences: A003598 A003599 A003600 this_sequence A003602 A003603 A003604
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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EXTENSIONS
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David W. Wilson (davidwwilson(AT)comcast.net), Oct 15 1996, points out that 30 was missing.
More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 03 2006
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