Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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