A169664 Numbers k divisible respectively by the sum of digits, the sum of the squares and the sum of the cubes of digits in base 10 of k.

1, 10, 100, 110, 111, 200, 500, 1000, 1010, 1011, 1100, 1101, 1110, 2000, 2352, 5000, 5500, 10000, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11100, 11112, 20000, 22000, 22200, 23520, 25032, 25110, 30100, 40000, 41013, 44160, 50000

Offset: 1

Author

Michel Lagneau, Apr 05 2010

Keywords

• nonn
• base

Examples

			For k = 174192, 1^3 + 7^3 + 4^3 + 1^3 + 9^3 + 2^3 = 1146, and 174192 = 152*1146; 1^2 + 7^2 + 4^2 + 1^2 + 9^2 + 2^2 = 152, and 174192 = 152*1146; 1 + 7 + 4 + 1 + 9 + 2 = 24, and 174192 = 24*7258.
		

Links

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

Crossrefs

Cf. A003132, A007953, A034087, A055012, A072081, A117562.

Programs

Maple

with(numtheory):for n from 1 to 200000 do:l:=evalf(floor(ilog10(n))+1) : n0:=n:s1:=0:s2:=0: s3:=0:for m from 1 to l do:q:=n0:u:=irem(q,10):v:=iquo(q,10):n0:=v :s1:=s1+u:s2:=s2+u^2:s3:=s3+u^3:od:if irem(n,s1)=0 and irem(n,s2)=0 and irem(n,s3)=0 then print(n):else fi:od:

Mathematica

dsQ[n_]:=Module[{idn=IntegerDigits[n]}, Divisible[n,Total[idn]] && Divisible[n,Total[idn^2]] && Divisible[n,Total[idn^3]]]; Select[Range[50000],dsQ]  (* Harvey P. Dale, Feb 24 2011 *)

Formula

A007953(k)|k and A003132(k)|k and A055012(k)| k.