%I A125650
%S A125650 1,5,9,7,5,27,35,11,27,65,77,45,26,119,135,38,85,189,209,115,63,275,299,
%T A125650 81,175,377,405,217,116,495,527,140,297,629,665,351,185,779,819,215,451,
%U A125650 945,989,517,270,1127,1175,306,637,1325,1377,715,371,1539,1595,413,855
%N A125650 Numerator of n(n+3)/(4(n+1)(n+2)) = Sum[ 1/(k(k+1)(k+2)), {k,1,n} ].
%C A125650 3^2 divides a(3k). p divides a(p) for an odd prime p. p divides a(p-3) 
               for prime p>3. p^k divides a(p^k) for an odd prime p. a(n) = m^2 
               is a perfect square for n = {1,3,24,147,864,5043,29400,171363,...} 
               = A125651(n). Corresponding numbers m such that m^2 = a[ A125651(n) 
               ] are listed in A125652(n) = {1,3,9,105,306,3567,10395,121173,...}.
%F A125650 a(n) = Numerator[ n(n+3)/(4(n+1)(n+2)) ].
%F A125650 a(n)=n*(n+3)/2^min(3,valuation(n*(n+3),2)). a(n)=n*(n+3)/4 for n=1 or 
               4 (mod 8); a(n)=n*(n+3)/8 for n=0 or 5 (mod 8); a(n)=n*(n+3)/2 for 
               n=2, 3, 6, or 7 (mod 8). - Max Alekseyev (maxale(AT)gmail.com), Jan 
               11 2007
%t A125650 Table[Numerator[n(n+3)/(4(n+1)(n+2))],{n,1,100}]
%o A125650 (PARI) a(n)=n*(n+3)/2^min(3,valuation(n*(n+3),2)) - Max Alekseyev (maxale(AT)gmail.com), 
               Jan 11 2007
%Y A125650 Cf. A125651, A125652.
%Y A125650 Sequence in context: A079459 A118309 A100106 this_sequence A140724 A086055 
               A077125
%Y A125650 Adjacent sequences: A125647 A125648 A125649 this_sequence A125651 A125652 
               A125653
%K A125650 nonn,frac
%O A125650 1,2
%A A125650 Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 29 2006