%I A126069
%S A126069 1,1,4,5,11,4,29,9,19,11,199,4,521,29,31,49,3571,19,9349,25,211,199,
%T A126069 64079,36,15251
%N A126069 Generates A001350, the associated Mersenne numbers; A001350(n)=Product[a(d)] 
               for d|n.
%D A126069 A 2001 Iranian Mathematical Olympiad question shows that such a generating 
               sequence {a(n)} exists for the sequence {S(n)} whenever gcd(S(m),
               S(n)) = S(gcd(m,n)).
%e A126069 The divisors of 6 are 1,2,3,6 and a(1)*a(2)*a(3)*a(6)=1*1*4*4=16, which 
               is, in fact, A001350(6).
%Y A126069 Cf. A001350, A061446.
%Y A126069 Sequence in context: A109675 A052508 A074098 this_sequence A147559 A007429 
               A064945
%Y A126069 Adjacent sequences: A126066 A126067 A126068 this_sequence A126070 A126071 
               A126072
%K A126069 nonn
%O A126069 1,3
%A A126069 John W. Layman (layman(AT)math.vt.edu), Feb 28 2007