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A254621 Zerofree numbers having product of digits less than or equal to sum of digits.

%I A254621 #38 Jun 29 2019 11:54:30
%S A254621 1,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18,19,21,22,31,41,51,61,71,81,
%T A254621 91,111,112,113,114,115,116,117,118,119,121,122,123,131,132,141,151,
%U A254621 161,171,181,191,211,212,213,221,231,311,312,321,411
%N A254621 Zerofree numbers having product of digits less than or equal to sum of digits.
%C A254621 Intersection of A052382 and A062996.
%C A254621 The repunit A002275(k), for k >= 2, appears  at position A254622(k-1) + 1. - _Wolfdieter Lang_, Feb 23 2015
%H A254621 David A. Corneth, <a href="/A254621/b254621.txt">Table of n, a(n) for n = 1..10000</a>
%p A254621 extend:= proc(t, b, d)
%p A254621   local i,j,m,s,p;
%p A254621   p:= t[2];
%p A254621   s:= t[3];
%p A254621   if s = 0  then if b=2 then j:= 3 else j:= 2 fi
%p A254621   else  for j from 0 to d-nops(t[1]) while p*b^j <= s + j*b do od
%p A254621   fi:
%p A254621   seq([[op(t[1]),b$i],p*b^i,s+i*b],i=0..j-1);
%p A254621 end proc:
%p A254621 f:= proc(d)
%p A254621    local j, b, Res;
%p A254621    Res:= [seq([[1$j],1,j],j=0..d)];
%p A254621    for b from 2 to 9 do
%p A254621      Res:= map(extend,Res,b,d)
%p A254621    od:
%p A254621    Res:= map(t -> op(combinat:-permute(t[1])),Res);
%p A254621    subs(0=NULL,sort(map(t -> add(t[i]*10^(i-1),i=1..nops(t)), Res)));
%p A254621 end proc:
%p A254621 f(5); # _Robert Israel_, May 19 2015
%t A254621 m[w_] := Flatten@Table[i, {i,9}, {w[[i]]}]; a[upd_] := Union@ Flatten@ Table[ FromDigits /@ Flatten[Permutations /@ m /@ Select[ Flatten[ Permutations /@ (IntegerPartitions[d + 9, {9}, Range[d + 1]] - 1), 1], Times @@ (Range[9]^#) <= Total[# Range[9]] &], 1], {d,  upd}]; a[12] (* terms with up to 12 digits, _Giovanni Resta_, May 19 2015 *)
%t A254621 zfnQ[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,0]&&Times@@idn <= Total[ idn]]; Select[Range[500],zfnQ] (* _Harvey P. Dale_, Jun 29 2019 *)
%o A254621 (PARI) is(n)={my(d=digits(n));my(p=prod(i=1,#d,d[i])); 0 < p && p<=vecsum(d) } \\ _David A. Corneth_, May 15 2015
%Y A254621 Cf. A052382, A062996, A062997, A062998, A062999, A254622, A002275.
%K A254621 nonn,base
%O A254621 1,2
%A A254621 _David A. Corneth_, Feb 03 2015