A191872 a(n) is the smallest multiple of n such that the sum of the square of the decimal digits of a(n) is divisible by n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 130, 1265, 60, 143, 154, 360, 48, 1071, 396, 133, 240, 693, 1386, 1817, 888, 50, 286, 999, 2408, 2552, 390, 372, 448, 1419, 2992, 315, 2268, 1295, 266, 3666, 480, 1148, 1344, 129, 11176, 360, 3818, 329, 8880, 2254, 550, 1071, 2444, 2597, 2268, 12485, 2688, 399, 2552, 12449, 111960, 549, 372, 693, 8000

Offset: 1

Author

Michel Lagneau, Jun 18 2011

Keywords

• nonn
• base

Examples

			a(11) =1265 because 11*115 = 1265 and 1^2+2^2+6^2+5^2 = 66 = 11*6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..467

Crossrefs

Cf. A002998, A131382.

Programs

Maple

with(numtheory):for n from 1 to 80 do:id:=0:for k from 1 to 1000000 while(id=0)
  do :l:=length(k):n0:=k:s1:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q,
  10):n0:=v :s1:=s1+u^2 :od: :if irem(k,n) =0 and irem(s1,n)=0 then id:=1:printf(`%d,
  `, k):else fi:od: od:

Mathematica

smn[n_]:=Module[{k=1},While[Mod[Total[IntegerDigits[k n]^2],n]!=0,k++];n k]; Array[smn,70] (* Harvey P. Dale, Feb 13 2023 *)

PARI

a(n)=my(s);forstep(k=n,9e9,n,s=eval(Vec(Str(k)));if(sum(i=1,#s,s[i]^2)%n==0,return(k))) \\ Charles R Greathouse IV, Jun 20 2011