A049101 Numbers m such that m divides (product of digits of m) * (sum of digits of m).

1, 2, 3, 4, 5, 6, 7, 8, 9, 15, 18, 24, 45, 48, 135, 144, 288, 378, 476, 756, 864, 1575, 39366, 69984, 139968

Offset

1,2

Comments

Next term if it exists is greater than 4*10^7. - Michel ten Voorde

Sequence is finite and bounded above by 10^84, since if 10^k <= n < 10^(k+1) (product of digits of n)*(sum of digits of n) <= k*9^(k+2) which is less than 10^k for k >= 84. - Henry Bottomley, May 18 2000

Numbers with a zero digit are not permitted. - Harvey P. Dale, Jul 16 2011

No further terms to 2.5*10^9. - Robert G. Wilson v, Jul 17 2011

Sequence is complete. - Giovanni Resta, Mar 20 2013

If product of digits is performed on nonzero digits only, then 1088 is also in the sequence. - Giovanni Resta, Mar 22 2013

Links

Table of n, a(n) for n=1..25.

Giovanni Resta, Method used to compute the full sequence

Example

139968 is in the sequence since it divides (1*3*9*9*6*8) * (1+3+9+9+6+8). - Giovanni Resta, Mar 20 2013

Maple

A049101:=proc(q) local a, b, c, n;
for n from 1 to q do
  a:=n; b:=0; c:=1; while a>0 do b:=b+(a mod 10); c:=c*(a mod 10); a:=trunc(a/10); od;
  if c>0 then if type(b*c/n, integer) then print(n); fi; fi; od; end:
A049101(139968); # Paolo P. Lava, Mar 22 2013

Mathematica

okQ[n_]:=Module[{idn=IntegerDigits[n]}, !MemberQ[idn, 0] && Divisible[ (Total[idn]*Times@@idn), n]] (* Harvey P. Dale, Jul 16 2011 *)
(* full sequence *) dig[nD_] := Block[{ric, sol = {}, check}, check[mu_, minN_] := Block[{di = DigitCount@minN, k = 1, r}, While[(r = mu/k) >= minN, If[IntegerQ[r] && DigitCount[r] == di, AppendTo[sol, r]]; k++]]; ric[n_, prod_, sum_, lastd_, cnt_] := Block[{t}, If[cnt == nD, check[prod*sum, n], Do[t = nD - cnt - 1; If[n*10^(t+1) <= d*prod*9^t*(sum + d + 9*t), ric[10*n + d, d*prod, d + sum, d, cnt + 1], Break[]], {d, 9, lastd, -1}]]]; ric[0, 1, 0, 1, 0]; Print["nDig=", nD, " sol=", sol = Sort@sol]; sol]; Flatten[dig /@ Range[84]] (* Giovanni Resta, Mar 20 2013 *)

Crossrefs

Cf. A038369, A049102, A049105, A049106.

Sequence in context: A032978 A197181 A260352 * A287336 A048406 A081433

Adjacent sequences: A049098 A049099 A049100 * A049102 A049103 A049104

Keyword

nonn,base,fini,full

Author

Olivier Gérard

Status

approved