%I A143578
%S A143578 1,2,3,5,7,11,13,15,17,19,23,29,31,35,37,41,43,47,53,59,61,67,71,73,79,
%T A143578 83,89,95,97,101,103,107,109,113,119,127,131,137,139,143,149,151,157,
%U A143578 163,167,173,179,181,191,193,197,199,209,211,223,227,229,233,239,241,251,
               257,263,269,271,277,281,283,287,293
%N A143578 A positive integer n is included if j+n/j divides k+n/k for every divisor 
               k of n, where j is the largest divisor of n that is <= sqrt(n).
%C A143578 This sequence trivially contains all the primes.
%C A143578 There is no term <= 5*10^7 with bigomega(n)>2, i.e. with more than 2 
               prime factors. - M. F. Hasler, Aug 25 2008. Compare A142591.
%C A143578 If it is always true that the terms have <= 2 prime divisors, then this 
               sequence is equal to {1} U primes U {pq: p, q prime, p+q | p^2-1}. 
               - David Wilson, Aug 25 2008
%H A143578 Leroy Quet, <a href="http://www.prism-of-spirals.net/">Home Page</a> 
               (listed in lieu of email address)
%e A143578 The divisors of 35 are 1,5,7,35. The sum of the two middle divisors is 
               5+7 = 12. 12 divides 7 + 35/7 = 5+35/5 = 12, of course. And 12 divides 
               1 + 35/1 = 35 +35/35 = 36. So 35 is in the sequence.
%t A143578 a = {}; For[n = 1, n < 200, n++, b = Max[Select[Divisors[n], # <= Sqrt[n] 
               &]]; If[ Length[Union[Mod[Divisors[n] + n/Divisors[n], b + n/b]]] 
               == 1, AppendTo[a, n]]]; a [From Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Aug 29 2008]
%o A143578 (PARI code from M. F. Hasler, Aug 25 2008) isA143578(n)={ local( d=divisors(n), 
               j=(1+#d)\2, r=d[ j ]+d[ 1+#d-j ]); for( k=1, j, ( d[k]+d[ #d+1-k] 
               ) % r & return ); 1 }
%o A143578 for(n=1,300,isA143578(n) && print1(n","))
%Y A143578 Cf. A063655, A142591.
%Y A143578 Sequence in context: A117287 A121615 A097605 this_sequence A086070 A117093 
               A062063
%Y A143578 Adjacent sequences: A143575 A143576 A143577 this_sequence A143579 A143580 
               A143581
%K A143578 nonn
%O A143578 1,2
%A A143578 Leroy Quet Aug 24 2008
%E A143578 More terms from M. F. Hasler, Aug 25 2008 and Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Aug 29 2008