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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 Cf. A188641, A188642. Sequence in context: A001102 A051004 A032575 * A118575 A327453 A289791 Adjacent sequences: A038183 A038184 A038185 * A038187 A038188 A038189 KEYWORD nonn,base,nice,look AUTHOR Felice Russo 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.)