A169662 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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) ;