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 A131456 #9 Feb 16 2025 08:33:06 %S A131456 1,2,1,2,1,2,1,2,1,2,1,4,1,2,1,2,1,2,1,2,1,2,1,6,1,2,1,2,1,2,1,2,1,2, %T A131456 1,4,1,2,1,2,1,2,1,2,1,2,1,8,1,2,1,2,1,2,1,2,1,2,1,7,1,2,1,2,1,2,1,2, %U A131456 1,2,1,6,1,2,1,2,1,2,1,2,1,2,1,4,1,2,1,2,1,2,1,2,1,2,1,10,1,2,1,2,1,2,1,2,7 %N A131456 Number of q-partial fraction summands of the reciprocal of n-th cyclotomic polynomial. %C A131456 Let Phi(n,q) be the n-th cyclotomic polynomial in q. The q-partial fraction decomposition of 1/Phi(n,q) is a representation of 1/Phi(n,q) as a finite sum of functions v(q)/(1-q^m)^t, such that m<=n and degree(v)<phi(m) (Euler's totient function A000010). %H A131456 Augustine O. Munagi, <a href="http://www.emis.de/journals/INTEGERS/papers/h25/h25.Abstract.html">Computation of q-partial fractions</a>, INTEGERS: Electronic Journal Of Combinatorial Number Theory, 7 (2007), #A25. %H A131456 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CyclotomicPolynomial.html">Cyclotomic Polynomial</a> %e A131456 (i) a(3)=1 because 1/Phi(3,q)=(1-q)/(1-q^3); %e A131456 (ii) a(6)=2 because 1/Phi(6,q)=(-1-q)/(1-q^3) + (2+2q)/(1-q^6). %Y A131456 Cf. A051664 (Number of terms in n-th cyclotomic polynomial). %K A131456 nonn %O A131456 1,2 %A A131456 _Augustine O. Munagi_, Jul 12 2007