A169663 Numbers k divisible by the sum of the digits and the sum of the squares of digits of k (in base 10).

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

Author

Michel Lagneau, Apr 05 2010

Keywords

• nonn
• base

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Digit.

Crossrefs

Cf. A003132, A007953, A034087, A072081, A117562.

Intersection of A005349 and A034087.

Programs

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 *)

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

Formula

A007953(k)|k and A003132(k)|k.