A078218 Smallest multiple of n that begins with the concatenation of the divisors of n (in increasing order).

1, 12, 132, 124, 15, 1236, 175, 1248, 1395, 12510, 1111, 12346128, 1131, 127148, 13515, 124816, 1173, 12369186, 1197, 12451020, 137214, 12112210, 12305, 1234681224, 1525, 1213264, 1392714, 1247142820, 12905, 12356101530, 13113

Offset: 1

Author

Amarnath Murthy, Nov 22 2002

Keywords

• base
• nonn
• look

Examples

			The concatenation of the divisors of 7 is 17; 175 = 25*7 is the smallest multiple of 7 that begins with 17, so a(7) = 175.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A037278, A069872, A078810.

Programs

Maple

cdiv:= proc(n) local D,R,j;
  D:= sort(convert(numtheory:-divisors(n),list));
  R:= D[1];
  for j from 2 to nops(D) do
    R:= R * 10^(1+ilog10(D[j])) + D[j];
  od;
  R
end proc:
f:= proc(n) local t,i,r;
  t:= cdiv(n);
  for i from 0 do
    r:= n * ceil(t*10^i/n);
    if r < (t+1)*10^i then return r fi
  od
end proc:
map(f, [$1..50]); # Robert Israel, Oct 07 2024

PARI

{for(n=1,31,k=floor(log(n)/log(10))+1; d=divisors(n); v=Str(); for(i=1,matsize(d)[2], v=concat(v,Str(d[i]))); s=eval(v); t=s+1; m=floor(log(s)/log(10))+1; d=k-m; s=s*10^d; t=t*10^d; b=1; while(b>0,q=floor(s/n); while(b>0&&(p=q*n)=s,print1(p,","); b=0,q++)); s=10*s; t=10*t))}

Extensions

Edited and extended by Klaus Brockhaus, Dec 06 2002