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