%I #2 Mar 30 2012 17:26:35
%S 1,2,1,2,1,3,1,2,1,2,1,4,1,2,1,4,1,4,1,2,3,2,3,4,2,3,3,2,3,3,1,4,1,4,
%T 1,4,1,4,1,2,2,4,4,2,5,4,2,4,4,2,1,2,1,6,1,8,1,2,1,6,3,3,3,4,3,3,3,4,
%U 3,2,1,4,1,2,1,4,1,4,1,2,4,2,4,4,2,4,4,2,4,3,1,4,1,4,1,4,1,4,1,2,2,3,3,2,3
%N a(n) are such that n or one of its substrings is divisible by every integer from 1 to a(n).
%C Positions of records 1,2,6,12,45,54,56,... are terms in A177834 (with repetitions).
%e a(56)=8 because divisors of 56 are d1={1,2,4,7,8,14,28,56},
%e divisors of 5 are d2={1, 5}, divisors of 6 are d3={1,2,3,6},
%e and union of d1, d2, d3 gives 8 subsequent integers 1..8 (14,28,.. not counted).
%t Table[id=IntegerDigits[n]; FLA=Flatten[Table[Partition[id, k, 1],
%t {k,Length[id]}], 1]; fd = Complement[Union[FromDigits /@ FLA], {0}];
%t dv=Union[Flatten[Divisors /@ fd]]; Complement[Range[100], dv][[1]]1, {n,10^3}]
%Y A177834.
%K base,nonn
%O 1,2
%A _Zak Seidov_, May 29 2010
