A082123 Smallest difference > 1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 17.

17, 16, 26, 36, 76, 94, 432, 37220, 996768, 158267352, 973348166592, 8429202561226344, 419324164827901536306744, 339991740461303603766175692597227316, 12025891484499365294341150949542442100059557280661504

Offset

1,1

Links

Table of n, a(n) for n=1..15.

Maple

branch:= proc(m, dm, bestyet)
    local t, x, nby, r;
    nby:= bestyet;
    for t from F[m][2] by -1 to 0 do
      x:= dm*F[m][1]^t;
      if x >= nby then next
      elif x >= c then nby:= x
      elif (x*R[m] < c) or (m=nF) then break
      else nby:= branch(m+1, x, nby);
      fi
    od;
    nby
end proc:
P:= 17: A[1]:= 17:
for n from 2 to 15 do
  c:= ceil(1/2+1/2*sqrt(5+4*P));
  while not type(c, integer) do Digits:= 2*Digits; c:= eval(c) od:
  F:= ifactors(P)[2]; nF:= nops(F);
  F:= sort(F, (s, t)->s[1]>t[1]);
  R:= [seq(mul(F[i][1]^F[i][2], i=j+1..nF), j=1..nF)];
  d:= branch(1, 1, P);
  A[n]:= d - P/d;
  P:= P*A[n]
od:
seq(A[n], n=1..15); # Robert Israel, May 20 2015

Prog

(PARI) p=17; print1(p, ", "); for(n=1, 13, r=floor(sqrt(p)); d1=1; d2=1; nE=omega(p); P=factor(p); E=P[, 2]; P=P[, 1]; forvec(v=vector(nE, i, [0, E[i]]), x=prod(k=1, nE, P[k]^v[k]); if(x<=r && x>=d2, d1=d2; d2=x, if(x<=d2 && x>=d1, d1=x))); difer=p/d2-d2; if(difer<=1, difer=p/d1-d1); print1(difer", "); p*=difer)

Crossrefs

Cf. A082120, A003681 (starts with 2, 3), A082124.

Sequence in context: A022973 A023459 A004458 * A368929 A273973 A172091

Adjacent sequences: A082120 A082121 A082122 * A082124 A082125 A082126

Keyword

nonn,hard,more

Author

Ralf Stephan, Apr 04 2003

Extensions

a(12) from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 02 2006

a(13) from Herman Jamke (hermanjamke(AT)fastmail.fm), Nov 14 2006

a(14) and a(15) from Robert Israel, May 20 2015

Status

approved