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

21, 4, 5, 13, 8, 2, 32, 16, 64, 512, 131072, 4194304, 8589934592, 9007199254740992, 75557863725914323419136, 20769187434139310514121985316880384

Offset: 0

Author

Ralf Stephan, Apr 04 2003

Keywords

• nonn
• hard

Comments

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

Crossrefs

Cf. A082120, A003681 (starts with 2, 3).

Programs

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]))