This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A027417 #68 Oct 13 2023 19:28:32
%S A027417 1,2,7,26,90,340,1238,4647,17578,67592,259768,1004348,3902357,
%T A027417 15202050,59410557,232483840,911689012,3581049040,14081089288,
%U A027417 55439171531,218457593223,861617935051,3400917861268,13433148229639,53092686926155,209962593513292
%N A027417 Number of distinct products i*j with 0 <= i, j <= 2^n - 1.
%C A027417 This is a subsequence of A027384.
%D A027417 R. P. Brent and H. T. Kung, The area-time complexity of binary multiplication, J. ACM 28 (1981), 521-534. Corrigendum: ibid 29 (1982), 904.
%D A027417 R. P. Brent, C. Pomerance, D. Purdum, and J. Webster, Algorithms for the multiplication table, Integers 21 (2021), paper #A92.
%H A027417 Richard P. Brent, <a href="/A027417/b027417.txt">Table of n, a(n) for n = 0..30</a>
%H A027417 Richard P. Brent, <a href="https://maths-people.anu.edu.au/~brent/pd/Brent-NTDU7.pdf">The Multiplication Table Problem Revisited</a>, Australian National University and CARMA, University of Newcastle (Australia, 2019).
%H A027417 R. P. Brent and H. T. Kung, <a href="http://wwwmaths.anu.edu.au/~brent/pub/pub055.html">The area-time complexity of binary multiplication</a>.
%H A027417 R. P. Brent and C. Pomerance, <a href="http://maths-people.anu.edu.au/~brent/pd/multiplication.pdf">The multiplication table, and random factored integers</a>, Presented at 56th Annual Meeting of Australian Math. Soc., Ballarat, Sept. 2012.
%H A027417 R. P. Brent and C. Pomerance, <a href="/A027424/a027424.pdf">The multiplication table, and random factored integers</a>, Presented at 56th Annual Meeting of Australian Math. Soc., Ballarat, Sept. 2012. [Cached copy, with permission]
%H A027417 R. P. Brent and C. Pomerance, <a href="http://maths-people.anu.edu.au/~brent/pd/multiplication-HK.pdf">Some mysteries of multiplication, and how to generate random factored integers</a>, Presented in Hong Kong, Feb. 2015.
%H A027417 R. P. Brent and C. Pomerance, <a href="/A027424/a027424_1.pdf">Some mysteries of multiplication, and how to generate random factored integers</a>, Presented in Hong Kong, Feb. 2015. [Cached copy, with permission]
%H A027417 R. P. Brent, C. Pomerance and J. Webster, <a href="http://maths-people.anu.edu.au/~brent/pd/multiplication-CARMA.pdf">Algorithms for the multiplication table problem</a>, Slides of a talk given in May 2018.
%H A027417 R. P. Brent, C. Pomerance, D. Purdum, and J. Webster, <a href="https://arxiv.org/abs/1908.04251">Algorithms for the multiplication table</a>, arXiv:1908.04251 [math.NT], 2019-2021.
%F A027417 a(n) = A027384(2^n-1). - _R. J. Mathar_, Jun 09 2016
%e A027417 For n = 2 we have a(2) = 7 because taking all products of the integers {0, 1, 2, 3 = 2^2 - 1} we get 7 distinct integers {0, 1, 2, 3, 4, 6, 9}.
%t A027417 Array[Length@ Union[Times @@@ Tuples[Range[0, 2^# - 1], {2}]] &, 12, 0] (* _Michael De Vlieger_, May 27 2018 *)
%o A027417 (Python)
%o A027417 def A027417(n): return len({i*j for i in range(1,1<<n) for j in range(1,i+1)})+1 # _Chai Wah Wu_, Oct 13 2023
%Y A027417 Cf. A027384, A027424.
%K A027417 nonn,hard
%O A027417 0,2
%A A027417 David Lambert (dlambert(AT)ichips.intel.com)
%E A027417 Corrected offset, added entries a(13)-a(25) and included a reference to a paper by Brent and Kung (1982) that gives the entries through a(17) by _Richard P. Brent_, Aug 20 2012