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A038186 Numbers divisible by the sum and product of their digits. 15
1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 111, 112, 132, 135, 144, 216, 224, 312, 315, 432, 612, 624, 735, 1116, 1212, 1296, 1332, 1344, 1416, 2112, 2232, 2916, 3132, 3168, 3276, 3312, 4112, 4224, 6624, 6912, 8112, 9612, 11112, 11115, 11133, 11172, 11232 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The property "numbers divisible by the sum and product of their digits" leads to the Diophantine equation t*x1*x2*...*xr=s*(x1+x2+...+xr), where t and s are divisors of n; xi is from [1...9]. This corresponds to some arithmetic problems in geometry, see Sándor, 2002. - Ctibor O. Zizka, Mar 04 2008
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10352 (first 1000 terms from T. D. Noe)
József Sándor, Geometric Theorems, Diophantine Equations and Arithmetic Functions, American Research Press, Rehoboth, 2002.
FORMULA
A188641(a(n)) * A188642(a(n)) = 1. - Reinhard Zumkeller, Apr 07 2011
MAPLE
P:=proc(n) local i, k, w, x; for i from 1 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; x:=1; k:=i; while k>0 do x:=x*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if x>0 then if i/x=trunc(i/x) and i/w=trunc(i/w) then print(i); fi; fi; od; end: P(1000); # Paolo P. Lava, Feb 12 2008
MATHEMATICA
dspQ[n_]:=Module[{idn=IntegerDigits[n], t}, t=Times@@idn; t!=0 && Divisible[n, Total[idn]] && Divisible[n, t]]; Select[Range[11500], dspQ] (* Harvey P. Dale, Jul 11 2011 *)
PROG
(Haskell)
import Data.List (elemIndices)
a038186 n = a038186_list !! (n-1)
a038186_list = map succ $ elemIndices 1
$ zipWith (*) (map a188641 [1..]) (map a188642 [1..])
-- Reinhard Zumkeller, Apr 07 2011
(PARI) for(n=1, 10^4, d=digits(n); s=sumdigits(n); p=prod(i=1, #d, d[i]); if(p&&!(n%s+n%p), print1(n, ", "))) \\ Derek Orr, Apr 29 2015
(Python)
from math import prod
def sd(n): return sum(map(int, str(n)))
def pd(n): return prod(map(int, str(n)))
def ok(n): return n%sd(n) == 0 and pd(n) and n%pd(n) == 0
def aupto(limit): return [m for m in range(1, limit+1) if ok(m)]
print(aupto(11233)) # Michael S. Branicky, Jan 28 2021
CROSSREFS
Intersection of A005349 and A007602. - Reinhard Zumkeller, Apr 07 2011
Sequence in context: A001102 A051004 A032575 * A118575 A327453 A289791
KEYWORD
nonn,base,nice,look
AUTHOR
EXTENSIONS
More terms from Patrick De Geest, Jun 15 1999
STATUS
approved

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Last modified December 11 13:16 EST 2023. Contains 367727 sequences. (Running on oeis4.)