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A169663
Numbers k divisible by the sum of the digits and the sum of the squares of digits of k (in base 10).
1
1, 10, 20, 50, 100, 110, 111, 120, 133, 200, 210, 240, 315, 360, 372, 400, 420, 480, 500, 550, 630, 803, 1000, 1010, 1011, 1020, 1071, 1100, 1101, 1110, 1134, 1148, 1200, 1300, 1302, 1330, 1344, 1431, 1547, 2000, 2010, 2023, 2040, 2100, 2196, 2200, 2220
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Digit.
FORMULA
A007953(k)|k and A003132(k)|k.
EXAMPLE
For k = 2196, 2^2 + 1^2 + 9^2 + 6^2 = 122, 2 + 1 + 9 + 6 = 18, and 2196 = 18*122 so it is divisible by both 18 and 122.
MAPLE
with(numtheory):for n from 1 to 1000000 do:l:=evalf(floor(ilog10(n))+1):n0:=n:s1:=0:s2:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v :s1:=s1+u:s2:=s2+u^2:od:if irem(n, s1)=0 and irem(n, s2)=0 then print(n):else fi:od:
MATHEMATICA
Select[Range[2220], Divisible[#, Plus @@ (d = IntegerDigits[#])] && Divisible[#, Plus @@ (d^2)] &] (* Amiram Eldar, Mar 04 2023 *)
PROG
(PARI) sd2(n) = my(d=digits(n)); sum(i=1, #d, d[i]^2);
isok(n) = !(n % sumdigits(n)) && !(n % sd2(n)); \\ Michel Marcus, Dec 21 2014
CROSSREFS
Intersection of A005349 and A034087.
Sequence in context: A072081 A034087 A117562 * A250602 A115045 A205879
KEYWORD
nonn,base
AUTHOR
Michel Lagneau, Apr 05 2010
STATUS
approved