A082126 Smallest difference>1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 19.

19, 18, 29, 27, 9, 27, 2187, 6561, 531441, 387420489, 7625597484987, 328256967394537077627, 381520424476945831628649898809, 235655016338368235499067731945871638181119123, 56392087339601733413306017749077372989860250021295987473736382457209

Offset

1,1

Comments

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

Links

Sean A. Irvine, Table of n, a(n) for n = 1..21

Prog

(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]))

Crossrefs

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

Sequence in context: A023461 A305238 A004460 * A176411 A131382 A291475

Adjacent sequences: A082123 A082124 A082125 * A082127 A082128 A082129

Keyword

nonn

Author

Ralf Stephan, Apr 04 2003

Extensions

Offset changed and more terms from Sean A. Irvine, Nov 24 2025

Status

approved