%I #15 Oct 14 2022 08:52:55

%S 1,101,202,404,606,1212,2424,7272,21816,41208,84048,123624,144144,

%T 336336,288288,504504,432432,865368,864864,1009008,2378376,1729728,

%U 3459456,3027024,4756752,6054048,9081072,11099088,12108096,16648632,23207184,29405376,36324288

%N a(n) is the smallest number that has exactly n divisors that are cyclops numbers (A134808).

%e The divisors of 101 are 1 and 101. Of those, only 101 is a cyclops number; it is the smallest cyclops number, so a(1) = 101.

%e The divisors of 202 are 1, 2, 101, and 202, the cyclops numbers being 101 and 202, so a(2) = 202.

%e The divisors of 404 are 1, 2, 4, 101, 202, and 404, the cyclops numbers being 101, 202 and 404, so a(3) = 404.

%p L:= Vector(10^8):

%p C:= [0]:

%p for d from 3 to 7 by 2 do

%p C:= [seq(seq(seq(a*10^(d-1)+10*b+c,c=1..9),b=C),a=1..9)];

%p for x in C do

%p Mx:= [seq(i,i=x..10^8,x)];

%p L[Mx]:= map(`+`,L[Mx],1)

%p od;

%p od:

%p V:= Array(0..max(L)):

%p for n from 1 to 10^8 do

%p if V[L[n]] = 0 then V[L[n]]:= n; fi

%p od:

%p if member(0,V,'k') then convert(V[0..k-1],list)

%p else convert(V,list)

%p fi; # _Robert Israel_, Sep 20 2022

%t cyclopQ[n_] := Module[{d = IntegerDigits[n], len}, OddQ[len = Length[d]] && Position[d, 0] == {{(len + 1)/2}}]; f[n_] := DivisorSum[n, 1 &, cyclopQ[#] &]; seq[len_, nmax_] := Module[{s = Table[0, {len}], c = 0, n = 1, i}, While[c < len && n < nmax, i = f[n] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = n]; n++]; s]; seq[10, 10^5] (* _Amiram Eldar_, Sep 26 2022 *)

%o (Magma) ints:=func<n|n eq 0 select [0] else Intseq(n)>; cyc:=func<n|IsOdd(#ints(n)) and ints(n)[(#ints(n)+1) div 2] eq 0 and Multiplicity(ints(n),0) eq 1>; a:=[]; for n in [0..32] do k:=1; while #[s:s in Divisors(k)| cyc(s)] ne n do k:=k+1; end while; Append(~a,k); end for; a;

%Y Cf. A134808.

%K nonn,base

%O 0,2

%A _Marius A. Burtea_, Sep 20 2022