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 A075753 #20 May 16 2025 02:43:30 %S A075753 1,3,3,3,3,5,7,3,3,3,3,11,5,3,3,3,3,5,19,3,3,3,3,23,5,3,3,3,3,29,31,3, %T A075753 3,3,3,5,37,3,3,3,3,41,5,3,3,3,3,5,7,3,3,3,3,53,5,3,3,3,3,7,11,3,3,3, %U A075753 3,5,7,3,3,3,3,11,5,3,3,3,3,5,79,3,3,3,3,83,5,3,3,3,3,89,7,3,3,3,3,5,97,3,3,3 %N A075753 Smallest prime factor of n-th odd triangular number; a(1) = 1. %C A075753 As A014493(n) = binomial(A042963(n),2) and a(n) = A020639(A014493(n)) > 2 for n > 1, A014493(n) is a good binomial coefficient. %H A075753 Amiram Eldar, <a href="/A075753/b075753.txt">Table of n, a(n) for n = 1..10000</a> %H A075753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GoodBinomialCoefficient.html">Good Binomial Coefficient</a>. %H A075753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LeastPrimeFactor.html">Least Prime Factor</a>. %H A075753 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>. %F A075753 From _Amiram Eldar_, May 16 2025: (Start) %F A075753 a(n) = A020639(A014493(n)). %F A075753 a(n) = A069901(A042963(n)). (End) %t A075753 FactorInteger[#][[1, 1]]&/@Select[Accumulate[Range[200]], OddQ] (* _Harvey P. Dale_, Jul 30 2016 *) %o A075753 (PARI) a(n) = if(n == 1, 1, factor((2*n-1)*(2*n-1-(-1)^n)/2)[1,1]); \\ _Amiram Eldar_, May 16 2025 %Y A075753 Cf. A014493, A020639, A042963, A069901. %K A075753 nonn,easy %O A075753 1,2 %A A075753 _Reinhard Zumkeller_, Mar 11 2003 %E A075753 a(1) inserted by _Amiram Eldar_, May 16 2025