%I A014567
%S A014567 1,2,3,4,5,7,8,9,11,13,16,17,19,21,23,25,27,29,31,32,35,36,37,39,41,43,
%T A014567 47,49,50,53,55,57,59,61,63,64,65,67,71,73,75,77,79,81,83,85,89,93,97,
%U A014567 98,100,101,103,107,109,111,113,115,119,121,125,127,128,129,131,133
%N A014567 Numbers n such that n and sigma(n) are relatively prime, where sigma(n) 
               = sum of divisors of n, A000203.
%C A014567 Related to "solitary numbers": n is solitary if there is no other integer 
               m such that sigma(m)/m = sigma(n)/n.
%C A014567 It is easy to show that if n and sigma(n) are relatively prime then n 
               is solitary. But the converse is not true; for example, 18, 45, 48 
               and 52 are solitary. Probably also 10, 14, 15, 20, 22 and many others 
               are solitary, but I do not think that will ever be proved. - Dean 
               Hickerson (dean.hickerson(AT)yahoo.com)
%C A014567 Contribution from Daniel Forgues (squid(AT)zensearch.com), Jun 23 2009: 
               (Start)
%C A014567 Union of unit, primes and Duffinian numbers.
%C A014567 Duffinian numbers (A003624) are the composite numbers (including, among 
               others, the composite prime powers) for which (n, sigma(n)) = 1. 
               (End)
%D A014567 Anderson, C. W. and Hickerson, D.; Problem 6020. ``Friendly Integers.'' 
               Amer. Math. Monthly 84, 65-66, 1977.
%H A014567 T. D. Noe, <a href="b014567.txt">Table of n, a(n) for n=1..1000</a>
%H A014567 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SolitaryNumber.html">Link to a section of The World of Mathematics.</
               a>
%e A014567 sigma(21) = 1+3+7+21 = 32 is relatively prime to 21.
%t A014567 lst={};Do[d=DivisorSigma[1, n];If[GCD[d, n]==1, AppendTo[lst, n]], {n, 
               6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 01 
               2008]
%Y A014567 Cf. A003624
%Y A014567 Sequence in context: A166401 A133811 A119314 this_sequence A030230 A089352 
               A086486
%Y A014567 Adjacent sequences: A014564 A014565 A014566 this_sequence A014568 A014569 
               A014570
%K A014567 nonn,easy,nice
%O A014567 1,2
%A A014567 Eric Weisstein (eric(AT)weisstein.com)
%E A014567 More terms from Labos Elemer (LABOS(AT)ana.sote.hu).