%I A126105
%S A126105 2,5,10,20,34,50,72,97,129,165,203,248,295,346,405,469,537,607,685,766,
%T A126105 843,949,1049,1155,1264,1376,1494,1620,1754,1897,2048,2193,2346,2503,
%U A126105 2669,2836,3012,3193,3378,3572,3770
%N A126105 Prime(n)^2*prime(n+1)...*prime(a(n)) is the least product of consecutive 
               primes which is abundant. Note that only the first term is squared.
%e A126105 a(3)=10 since x=5^2*7*11*13*17*19*23*29=5391411025 is abundant with sigma(x)=10799308800 
               and sigma(x)-2*x=16486750.
%t A126105 Search[n_] := Module[{}, k =n; While[DivisorSigma[1, Product[ Prime[i], 
               {i, n + 1, k}]*Prime[n]^2] <= 2*Product[Prime[i], {i, n + 1, k}]*Prime[n]^2, 
               k++ ]; k]; Table[Search[i], {i, 1, 15}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               May 11 2007
%Y A126105 Cf. A005101, A007684 (a very similar sequence), A007708, A007741.
%Y A126105 Sequence in context: A018327 A000099 A039690 this_sequence A117486 A000710 
               A117487
%Y A126105 Adjacent sequences: A126102 A126103 A126104 this_sequence A126106 A126107 
               A126108
%K A126105 less,nonn
%O A126105 1,1
%A A126105 Walter A. Kehowski (wkehowski(AT)cox.net), Mar 04 2007
%E A126105 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               May 11 2007