%I A159907
%S A159907 2,24,4320,4680,26208,8910720,17428320,20427264,91963648,197064960,
%T A159907 8583644160,10200236032,21857648640,57575890944,57629644800,
%U A159907 206166804480,17116004505600,1416963251404800,15338300494970880
%N A159907 Numbers n with half-integral abundancy index, sigma(n)/n = k+1/2 with 
               integer k.
%C A159907 Obviously, all a(k) must be even (cf. formula), but e.g. a(9) and a(12) 
               are not divisible by 3. See A007691 for numbers with integral abundancy.
%H A159907 Walter Nissen, <a href="http://upforthecount.com/math/abundance.html">
               Abundancy : Some Resources </a>
%F A159907 A159907 = { n | 2*A000203(n) is in n*A005408 } = { n | A054024(n) = n/
               2 }
%e A159907 a(1) = 2 since sigma(2)/2 = (1+2)/2 = 3/2 is of the form k+1/2 with integer 
               k=1.
%e A159907 Odd numbers and higher powers of 2 cannot be in the sequence; 6 is in 
               A000396 and thus in A007691, and n=10,12,14,18,20,22 don't have integral 
               2*sigma(n)/n.
%e A159907 a(2) = 24 is in the sequence since sigma(24)/24 = (1+2+3+4+6+8+12+24)/
               24 = (24+12+24)/24 = k+1/2 with integer k=2.
%Y A159907 Cf. A000203, A088912, A141643 (k=2), A055153 (k=3), A141645 (k=4), A159271 
               (k=5).
%Y A159907 Sequence in context: A111430 A059332 A000794 this_sequence A088912 A055462 
               A088600
%Y A159907 Adjacent sequences: A159904 A159905 A159906 this_sequence A159908 A159909 
               A159910
%K A159907 nonn
%O A159907 1,1
%A A159907 M. F. Hasler (MHasler(AT)univ-ag.fr), Apr 25 2009