A051004 Numbers divisible both by their individual digits and by the sum of their digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 24, 36, 48, 111, 112, 126, 132, 135, 144, 162, 216, 222, 224, 264, 288, 312, 315, 324, 333, 336, 396, 432, 444, 448, 555, 612, 624, 648, 666, 735, 777, 864, 888, 936, 999, 1116, 1122, 1128, 1164, 1212, 1224, 1236, 1296, 1332

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• nice
• base

Comments

No zero digits permitted. [Harvey P. Dale, Dec 18 2011]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digit

Crossrefs

Intersection of A005349 and A034838.

Cf. A038369, A087142.

Programs

Haskell

a051004 n = a051004_list !! (n-1)
a051004_list =  [x | x <- a005349_list,
                     x == head (dropWhile (< x) a034838_list)]
-- Reinhard Zumkeller, Mar 03 2012

Mathematica

ddQ[n_]:=Module[{idn=IntegerDigits[n]},!MemberQ[idn,0] && Divisible[ n,Total[idn]]&& And @@ Divisible[n,idn]]; Select[Range[1400],ddQ] (* Harvey P. Dale, Dec 18 2011 *)

Extensions

Offset corrected by Reinhard Zumkeller, Mar 03 2012