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

1,2

Links

Table of n, a(n) for n=1..64.

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A002998, A131382.

Sequence in context: A173689 A004871 A059405 * A280355 A001104 A151544

Adjacent sequences: A191869 A191870 A191871 * A191873 A191874 A191875

Keyword

nonn,base

Author

Michel Lagneau, Jun 18 2011

Status

approved