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A169662
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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.
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2
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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
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OFFSET
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1,2
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COMMENTS
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The numbers such that all digits are nonzero are rare (see the subsequence A176194).
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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;
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MATHEMATICA
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q[n_] := And @@ Divisible[n, Plus @@@ Transpose @ Map[#^Range[4] &, IntegerDigits[n]]]; Select[Range[10^5], q] (* Amiram Eldar, Jan 31 2021 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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