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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Intersection of A005349, A034087, A034088 and A169665.

Cf. A072081, A117562, A176194.

Sequence in context: A169664 A174417 A169666 * A124252 A121030 A327786

Adjacent sequences: A169659 A169660 A169661 * A169663 A169664 A169665

Keyword

nonn,base

Author

Michel Lagneau, Apr 05 2010

Status

approved