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%I #6 Oct 31 2023 11:05:22
%S 1,1,4,5,11,4,29,9,19,11,199,4,521,29,31,49,3571,19,9349,25,211,199,
%T 64079,36,15251
%N Generates A001350, the associated Mersenne numbers; A001350(n)=Product[a(d)] for d|n.
%C 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 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 Cf. A001350, A061446.
%K nonn
%O 1,3
%A _John W. Layman_, Feb 28 2007
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