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A357033
a(n) is the smallest number that has exactly n divisors that are cyclops numbers (A134808).
0
1, 101, 202, 404, 606, 1212, 2424, 7272, 21816, 41208, 84048, 123624, 144144, 336336, 288288, 504504, 432432, 865368, 864864, 1009008, 2378376, 1729728, 3459456, 3027024, 4756752, 6054048, 9081072, 11099088, 12108096, 16648632, 23207184, 29405376, 36324288
OFFSET
0,2
EXAMPLE
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.
The divisors of 202 are 1, 2, 101, and 202, the cyclops numbers being 101 and 202, so a(2) = 202.
The divisors of 404 are 1, 2, 4, 101, 202, and 404, the cyclops numbers being 101, 202 and 404, so a(3) = 404.
MAPLE
L:= Vector(10^8):
C:= [0]:
for d from 3 to 7 by 2 do
C:= [seq(seq(seq(a*10^(d-1)+10*b+c, c=1..9), b=C), a=1..9)];
for x in C do
Mx:= [seq(i, i=x..10^8, x)];
L[Mx]:= map(`+`, L[Mx], 1)
od;
od:
V:= Array(0..max(L)):
for n from 1 to 10^8 do
if V[L[n]] = 0 then V[L[n]]:= n; fi
od:
if member(0, V, 'k') then convert(V[0..k-1], list)
else convert(V, list)
fi; # Robert Israel, Sep 20 2022
MATHEMATICA
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 *)
PROG
(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;
CROSSREFS
Cf. A134808.
Sequence in context: A081365 A138131 A069858 * A319744 A303575 A171798
KEYWORD
nonn,base
AUTHOR
Marius A. Burtea, Sep 20 2022
STATUS
approved