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Search: id:A074902
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| A074902 |
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Known friendly numbers. |
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+0
10
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| 6, 12, 24, 28, 30, 40, 42, 56, 60, 66, 78, 80, 84, 96, 102, 108, 114, 120, 132, 135, 138, 140, 150, 168, 174, 186, 200, 204, 210, 222, 224, 228, 234, 240, 246, 252, 258, 264, 270, 273, 276, 280, 282, 294, 300, 308, 312, 318, 330, 348, 354, 360, 364, 366, 372
(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 is not known to be complete up to 372, since there are many small numbers, including 10, 14, 15 and 20, which have not been proved to be solitary. If any other numbers up to 372 are friendly, the smallest corresponding values of m are > 10^30.
A positive integer n is 'friendly' if abundancy(n) = abundancy(m) for some positive integer m not equal to n, where abundancy(n) = sigma(n)/n (cf. A000203); otherwise n is 'solitary'. (The name "friendly" is also sometimes mistakenly used with other meanings; cf. A063990 and A007770.)
All perfect numbers are friendly numbers, but they are only friendly with each other (a perfect number being defined as having abundancy index of 2.) [From Daniel Forgues (squid(AT)zensearch.com), Jun 23 2009]
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REFERENCES
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Claude W. Anderson and Dean Hickerson, Problem 6020: Friendly Integers, Amer. Math. Monthly 84 (1977) 65-66
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LINKS
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Eric Weisstein's World of Mathematics, Friendly Pair
Eric Weisstein's World of Mathematics, Friendly Number
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EXAMPLE
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24 is in the sequence since abundancy(24) = abundancy(91963648) = 5/2.
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CROSSREFS
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Union of A050972 and A050973. Cf. A014567.
Sequence in context: A081512 A096387 A094185 this_sequence A096366 A061822 A119840
Adjacent sequences: A074899 A074900 A074901 this_sequence A074903 A074904 A074905
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2002
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EXTENSIONS
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Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 19 2002
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