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A175516 a(n) = smallest positive even integer k such that k or one of its left substrings is divisible by any integer from {1..n}.

%I A175516 #13 Jun 10 2023 03:09:18
%S A175516 2,2,6,12,60,60,252,504,504,504,7260,7260,10296,11760,11760,11760,
%T A175516 56160,56160,198016,198016,1176480,1323008,2992500,6240366,13442580,
%U A175516 13442580,37536408,37536408,90725804,90725804,319800096,319800096,319800096,800640126,2201169600,2201169600,4656965040,5250966084,5250966084
%N A175516 a(n) = smallest positive even integer k such that k or one of its left substrings is divisible by any integer from {1..n}.
%H A175516 Hugo van der Sanden, <a href="https://github.com/hvds/seq/tree/master/A169858">A169858</a>: C source code to calculate terms (has an option to compute A175516).
%o A175516 (Python)
%o A175516 from itertools import count, islice
%o A175516 def agen(): # generator of terms
%o A175516     n = 1
%o A175516     for k in count(2, 2):
%o A175516         s = str(k)
%o A175516         prefixes = [int(s[:i+1]) for i in range(len(s))]
%o A175516         if all(any(ki%m == 0 for ki in prefixes) for m in range(3, n+1)):
%o A175516             yield k; n += 1
%o A175516             while any(ki%n == 0 for ki in prefixes):
%o A175516                 yield k; n += 1
%o A175516 print(list(islice(agen(), 20))) # _Michael S. Branicky_, Jun 09 2023
%Y A175516 Cf. A169858.
%K A175516 base,nonn
%O A175516 1,1
%A A175516 _Zak Seidov_, Jun 03 2010
%E A175516 Corrected and extended by _Hugo van der Sanden_, Jun 01 2010