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A082128 Smallest difference>1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 21. 2

%I #9 Mar 11 2015 07:43:26

%S 21,4,5,13,8,2,32,16,64,512,131072,4194304,8589934592,

%T 9007199254740992,75557863725914323419136,

%U 20769187434139310514121985316880384

%N Smallest difference>1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 21.

%C For n>3, the members are all powers of two. Proved by Luke Pebody, pers. comm.

%o (PARI) p=21; 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).

%K nonn,hard

%O 0,1

%A _Ralf Stephan_, Apr 04 2003

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Last modified July 21 06:08 EDT 2024. Contains 374463 sequences. (Running on oeis4.)