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.

1, 10, 100, 110, 111, 1000, 1010, 1011, 1100, 1101, 1110, 2000, 5000, 10000, 10010, 10011, 10100, 10101, 10110, 11000, 11001, 11010, 11100, 20000, 50000, 55000, 100000, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101100

Offset: 1

Author

Michel Lagneau, Apr 05 2010

Keywords

• nonn
• base

Comments

The numbers such that all digits are nonzero are rare (see the subsequence A176194).

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A005349, A034087, A034088 and A169665.

Cf. A072081, A117562, A176194.

Programs

Maple

isA169662 := proc(n)
        dgs := convert(n,base,10) ;
        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
                true;
        else
                false;
        end if;
end proc:
for i from 1 to 110000 do
        if isA169662(i) then
                printf("%d,",i) ;
        end if;
end do: # R. J. Mathar, Nov 07 2011

Mathematica

q[n_] := And @@ Divisible[n, Plus @@@ Transpose @ Map[#^Range[4] &, IntegerDigits[n]]]; Select[Range[10^5], q] (* Amiram Eldar, Jan 31 2021 *)

Formula

{n : A007953(n)|n and A003132(n)|n and A055012(n)| n and A055013(n)| n}.