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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.
2
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
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.
Sequence in context: A169664 A174417 A169666 * A124252 A121030 A327786
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 05 2010
STATUS
approved