%I #8 Mar 11 2015 07:26:18

%S 19,18,29,27,9,27,2187,6561,531441,387420489,7625597484987,

%T 328256967394537077627,381520424476945831628649898809,

%U 235655016338368235499067731945871638181119123

%N Smallest difference>1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 19.

%C Except for the first three, the members are all powers of 3. Proved by Luke Pebody, pers. comm.

%o (PARI) p=19; print1(p, ", "); for(n=1, 50, v=divisors(p); r=sqrt(p); t=0; for(k=1, matsize(v)[2], if(v[k]>=r, t=k; break)); if(v[t]^2==p, u=t, u=t-1); if(v[t]-v[u]<2, u=u-1; t=t+1); print1(v[t]-v[u]", "); p=p*(v[t]-v[u]))

%Y Cf. A082120, A003681 (starts with 2, 3), A082128.

%K nonn

%O 0,1

%A _Ralf Stephan_, Apr 04 2003