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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.

%I A169664 #24 Feb 16 2025 08:33:11
%S A169664 1,10,100,110,111,200,500,1000,1010,1011,1100,1101,1110,2000,2352,
%T A169664 5000,5500,10000,10010,10011,10100,10101,10110,11000,11001,11010,
%U A169664 11100,11112,20000,22000,22200,23520,25032,25110,30100,40000,41013,44160,50000
%N 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.
%H A169664 Amiram Eldar, <a href="/A169664/b169664.txt">Table of n, a(n) for n = 1..10000</a>
%H A169664 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Digit.html">Digit</a>.
%F A169664 A007953(k)|k and A003132(k)|k and A055012(k)| k.
%e A169664 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.
%p A169664 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:
%t A169664 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 *)
%Y A169664 Cf. A003132, A007953, A034087, A055012, A072081, A117562.
%K A169664 nonn,base
%O A169664 1,2
%A A169664 _Michel Lagneau_, Apr 05 2010