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A074902
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Known friendly numbers.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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.) - Daniel Forgues, Jun 23 2009
Triangle A211679 has rows that list the first numbers that have n-1 smaller friends. Sequence A211677 lists just the last number in each row. - T. D. Noe, May 10 2012
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LINKS
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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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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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