Search: id:A074902
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%I A074902
%S A074902 6,12,24,28,30,40,42,56,60,66,78,80,84,96,102,108,114,120,132,135,138,
%T A074902 140,150,168,174,186,200,204,210,222,224,228,234,240,246,252,258,264,
%U A074902 270,273,276,280,282,294,300,308,312,318,330,348,354,360,364,366,372
%N A074902 Known friendly numbers.
%C A074902 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.
%C A074902 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.)
%C A074902 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]
%D A074902 Claude W. Anderson and Dean Hickerson, Problem 6020: Friendly Integers, 
               Amer. Math. Monthly 84 (1977) 65-66
%H A074902 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FriendlyPair.html">Friendly Pair</a>
%H A074902 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FriendlyNumber.html">Friendly Number</a>
%e A074902 24 is in the sequence since abundancy(24) = abundancy(91963648) = 5/2.
%Y A074902 Union of A050972 and A050973. Cf. A014567.
%Y A074902 Sequence in context: A081512 A096387 A094185 this_sequence A096366 A061822 
               A119840
%Y A074902 Adjacent sequences: A074899 A074900 A074901 this_sequence A074903 A074904 
               A074905
%K A074902 nonn
%O A074902 1,1
%A A074902 N. J. A. Sloane (njas(AT)research.att.com), Sep 15 2002
%E A074902 Edited by Dean Hickerson (dean.hickerson(AT)yahoo.com), Sep 19 2002

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