login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A049101 Numbers n such that n divides (product of digits of n) * (sum of digits of n). 8
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 (list; graph; refs; listen; history; text; internal format)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 07:41 EST 2020. Contains 331241 sequences. (Running on oeis4.)