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 A082123 Smallest difference > 1 between d and p/d for any divisor d of the partial product p of the sequence, starting with 17. 2
 17, 16, 26, 36, 76, 94, 432, 37220, 996768, 158267352, 973348166592, 8429202561226344, 419324164827901536306744, 339991740461303603766175692597227316, 12025891484499365294341150949542442100059557280661504 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 * A273973 A172091 A291370 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

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)