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 A109054 #29 Jul 16 2021 05:22:44 %S A109054 0,1,3,4,7,8,9,13,14,15,16,22,23,24,25,32,33,34,35,36,44,47,48,49,58, %T A109054 59,60,62,63,64,74,75,78,79,80,81,95,96,98,99,100,114,119,120,121,135, %U A109054 136,138,140,141,142,143,144,160,162,164,167,168,169,185,187,189,192 %N A109054 Squares and numbers k such that the continued fraction expansion of sqrt(k) is multiplicative. %C A109054 If we consider each square k as having a continued fraction expansion c of all zeros after c(0) = sqrt(k)-1, then the continued fraction expansion of sqrt(k) for each square is trivially multiplicative. %C A109054 For nonsquares, c(1) must be 1 and so k must satisfy m + 1/2 < sqrt(k) <= m+1, for some integer m. %e A109054 The continued fraction of sqrt(22) is c = (4; 1, 2, 4, 2, 1, 8, ...) = A010126, which is multiplicative with c(2^e) = 2, c(3^e) = 4, c(p^e) = 1 otherwise. %Y A109054 Union of A000290 and A108575. %Y A109054 Continued fraction expansions: A040001, A010121, A040005, etc. %K A109054 nonn,easy %O A109054 1,3 %A A109054 _Mitch Harris_, Jun 18 2005