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A178544 a(n) are such that n or one of its substrings is divisible by every integer from 1 to a(n).

%I A178544 #2 Mar 30 2012 17:26:35
%S A178544 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 A178544 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 A178544 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 A178544 a(n) are such that n or one of its substrings is divisible by every integer from 1 to a(n).
%C A178544 Positions of records 1,2,6,12,45,54,56,... are terms in A177834 (with repetitions).
%e A178544 a(56)=8 because divisors of 56 are d1={1,2,4,7,8,14,28,56},
%e A178544 divisors of 5 are d2={1, 5}, divisors of 6 are d3={1,2,3,6},
%e A178544 and union of d1, d2, d3 gives 8 subsequent integers 1..8 (14,28,.. not counted).
%t A178544 Table[id=IntegerDigits[n]; FLA=Flatten[Table[Partition[id, k, 1],
%t A178544 {k,Length[id]}], 1]; fd = Complement[Union[FromDigits /@ FLA], {0}];
%t A178544 dv=Union[Flatten[Divisors /@ fd]]; Complement[Range[100], dv][[1]]-1, {n,10^3}]
%Y A178544 A177834.
%K A178544 base,nonn
%O A178544 1,2
%A A178544 _Zak Seidov_, May 29 2010