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A045544 Odd values of n for which a regular n-gon can be constructed by compass and straightedge.

%I A045544 #43 Aug 09 2024 01:56:20
%S A045544 3,5,15,17,51,85,255,257,771,1285,3855,4369,13107,21845,65535,65537,
%T A045544 196611,327685,983055,1114129,3342387,5570645,16711935,16843009,
%U A045544 50529027,84215045,252645135,286331153,858993459,1431655765,4294967295
%N A045544 Odd values of n for which a regular n-gon can be constructed by compass and straightedge.
%C A045544 If there are no more Fermat primes, then 4294967295 is the last term in the sequence.
%C A045544 From _Daniel Forgues_, Jun 17 2011: (Start)
%C A045544 The 31 = 2^5 - 1 terms of this sequence are the nonempty products of distinct Fermat primes. The 5 known Fermat primes are in A019434.
%C A045544 Prepending the empty product, i.e., 1, to this sequence gives A004729.
%C A045544 The initial term for this sequence is thus a(1) (offset=1), since a(0) should correspond to the omitted empty product, term a(0) of A004729.
%C A045544 Rows 1 to 31 of Sierpiński's triangle, if interpreted as a binary number converted to decimal (A001317), give a(1) to a(31). (End)
%D A045544 Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 73 at pp. 181-182.
%H A045544 Wilfrid Keller, <a href="http://www.prothsearch.com/fermat.html">Prime factors k.2^n + 1 of Fermat numbers F_m</a>.
%H A045544 OEIS Wiki, <a href="/wiki/Constructible_odd-sided_polygons">Constructible odd-sided polygons</a>.
%H A045544 OEIS Wiki, <a href="/wiki/Sierpinski&#39;s_triangle">Sierpinski's triangle</a>.
%F A045544 Each term is the product of distinct odd Fermat primes.
%F A045544 Sum_{n>=1} 1/a(n) = -1 + Product_{n>=1} (1+1/A019434(n)) = 0.7007354948... >= 1003212011/1431655765 = sigma(2^32-1)/(2^32-1) - 1, with equality if there are only five Fermat primes (A019434). - _Amiram Eldar_, Jan 22 2022
%t A045544 Union[Times@@@Rest[Subsets[{3,5,17,257,65537}]]] (* _Harvey P. Dale_, Sep 20 2011 *)
%Y A045544 Cf. A019434. Essentially same as A004729.
%Y A045544 Coincides with A001317 for the first 31 terms only. - _Robert G. Wilson v_, Dec 22 2001
%Y A045544 Cf. A053576.
%K A045544 hard,nonn,nice
%O A045544 1,1
%A A045544 _Ken Takusagawa_