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 A316780 #12 Nov 17 2019 01:56:29 %S A316780 1,1,1,1,3,1,3,1,3,1,3,1,5,1,3,7,1,7,3,9,3,3,1,9,9,3,11,1,5,5,13,3,1, %T A316780 15,15,5,1,17,3,5,1,17,7,3,17,1,7,19,1,21,3,5,7,23,5,1,25,9,1,5,25,9, %U A316780 27,3,27,1,29,5,11,29,3,11,1,11,5,3,33,1,35,13 %N A316780 a(n) is the least positive integer k such that ceiling(sqrt(A046315(n)*k))^2 - A046315(n)*k is a square. %C A316780 Fermat's factorization helper multiplier for the n-th odd semiprime. %C A316780 a(n) is the least positive integer such that A046315(n) * a(n) can be factorized with a single iteration of Fermat's factorization method. Using the factorization of a(n), we can then deduce the prime factors of A046315(n). Example for n = 35490: A046315(n) = 199163 and a(n) = 40; ceiling(sqrt(199163*40)) = 2823; 199163*40 = 2823^2 - 2809 = 2823^2 - 53^2 = (2823+53)(2823-53) = 2876*2770, leading to 199163*(2*2*2*5) = (2*2*719)*(2*5*277) and eventually 199163 = 719*277. %e A316780 a(18) = 7 because the 18th odd semiprime is A046315(18) = 93, ceiling(sqrt(93*7))^2 - 93*7 = 25 is a perfect square and 7 is the least positive integer for which this holds. %Y A316780 Cf. A046315. %K A316780 nonn %O A316780 1,5 %A A316780 _Arnauld Chevallier_, Jul 13 2018