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%I #11 May 18 2020 06:56:02
%S 1,30,60,840,10080,110880,1441440,15135120,21162960,21162960,
%T 232792560,26771144400,26771144400,2730656728800,30278164316400,
%U 33977306563200,38000934972000,3610088822340000,37400520199442400,390033996365613600,438120379479182400,4505020423775071200
%N a(n) is the smallest number which has n consecutive divisors k, k+1, ..., k+n-1 such that the quotients all begin with the same digit.
%C The smallest values of k corresponding to the first 22 terms are 1, 2, 4, 5, 6, 6, 8, 8, 12, 12, 12, 14, 14, 14, 16, 18, 20, 19, 19, 20, 22, 24. Since m > 0 and 2*m never share the first digit, k is always greater than or equal to n. - _Giovanni Resta_, May 14 2020
%H Denis Borris, <a href="https://web.archive.org/web/20060917004135/http://www.ecst.csuchico.edu/~kend/potw/archive/000215sol.html">Close Divisors</a>, Ken Duisenberg's Puzzle of the Week, Feb 20 2000.
%e a(4)=840 since 840/5=168, 840/6=140, 840/7=120 and 840/8=105 all start with 1.
%Y Cf. A000142.
%K nonn,base
%O 1,2
%A _Henry Bottomley_, Feb 22 2000
%E a(1) prepended and a(11)-a(22) added by _Giovanni Resta_, May 14 2020
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