cp's OEIS Frontend

A169662 Numbers divisible by the sum of their digits, and by the sum of their digits squared, by the sum of their digits cubed and by the sum of 4th powers of their digits.

%I A169662 #19 Jan 31 2021 02:38:02
%S A169662 1,10,100,110,111,1000,1010,1011,1100,1101,1110,2000,5000,10000,10010,
%T A169662 10011,10100,10101,10110,11000,11001,11010,11100,20000,50000,55000,
%U A169662 100000,100010,100011,100100,100101,100110,101000,101001,101010,101100
%N A169662 Numbers divisible by the sum of their digits, and by the sum of their digits squared, by the sum of their digits cubed and by the sum of 4th powers of their digits.
%C A169662 The numbers such that all digits are nonzero are rare (see the subsequence A176194).
%H A169662 Amiram Eldar, <a href="/A169662/b169662.txt">Table of n, a(n) for n = 1..10000</a>
%F A169662 {n : A007953(n)|n and A003132(n)|n and A055012(n)| n and A055013(n)| n}.
%e A169662 1121211 is a term since 1^4 + 1^4 + 2^4 + 1^4 + 2^4 + 1^4 + 1^4 = 37 and 1121211 = 37*30303 ; 1^3 + 1^3 + 2^3 + 1^3 + 2^3 + 1^3 + 1^3 = 21 and 1121211 = 21*53391 ; 1^2 + 1^2 + 2^2 + 1^2 + 2^2 + 1^2 + 1^2 = 13 and 1121211 = 13* 86247 ; 1 + 1 + 2 + 1 + 2 + 1 + 1 = 9 and 1121211 = 9*124579.
%p A169662 isA169662 := proc(n)
%p A169662         dgs := convert(n,base,10) ;
%p A169662         if (n mod ( add(d,d=dgs) ) = 0)  and (n mod (add(d^2,d=dgs) )) =0 and (n mod (add(d^3,d=dgs))) =0 and (n mod (add(d^4,d=dgs))) = 0 then
%p A169662                 true;
%p A169662         else
%p A169662                 false;
%p A169662         end if;
%p A169662 end proc:
%p A169662 for i from 1 to 110000 do
%p A169662         if isA169662(i) then
%p A169662                 printf("%d,",i) ;
%p A169662         end if;
%p A169662 end do: # _R. J. Mathar_, Nov 07 2011
%t A169662 q[n_] := And @@ Divisible[n, Plus @@@ Transpose @ Map[#^Range[4] &, IntegerDigits[n]]]; Select[Range[10^5], q] (* _Amiram Eldar_, Jan 31 2021 *)
%Y A169662 Intersection of A005349, A034087, A034088 and A169665.
%Y A169662 Cf. A072081, A117562, A176194.
%K A169662 nonn,base
%O A169662 1,2
%A A169662 _Michel Lagneau_, Apr 05 2010