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 A199972 #8 Jan 23 2025 10:25:10 %S A199972 0,0,4,9,19,29,41,55,71,89,109,131,155,181,209,239,271,305,341,379, %T A199972 419,461,505,551,599,649,701,755,811,869,929,991,1055,1121,1189,1259, %U A199972 1331,1405,1481,1559,1639,1721,1805,1891,1979,2069 %N A199972 a(n) = the sum of GCQ_B(n, k) for 1 <= k <= n (see definition in comments). %C A199972 Definition of GCQ_B: The greatest common non-divisor of type B (GCQ_B) of two positive integers a and b (a<=b) is the largest positive non-divisor q of numbers a and b such that 1<=q<=b common to a and b; GCQ_B(a, b) = 0 if no such c exists. %C A199972 For b>=5 holds: GCQ_B(a, b) = b - 1 if a = b or a<= b-2, GCQ_B(a, b) = b - 2 if a = b-1. %F A199972 a(n) = n*(n-1) - 1 for n>= 5. %e A199972 For n = 4, a(4) = 9 because GCQ_B(4, 1) = 3, GCQ_B(4, 2) = 3, GCQ_B(4, 3) = 0, GCQ_B(4, 4) = 3 and sum of results is 9. %e A199972 For n = 5, a(4) = 19 because GCQ_B(5, 1) = 4, GCQ_B(5, 2) = 4, GCQ_B(5, 3) = 4, GCQ_B(5, 4) = 3, GCQ_B(5, 5) = 4 and sum of results is 19. %Y A199972 Cf.: A196443 (the sum of GCQ_A(n, k) for 1 <= k <= n). %Y A199972 Cf.: A199973 (the sum of LCQ_B(n, k) for 1 <= k <= n). %Y A199972 Cf.: A199971 (the sum of LCQ_A(n, k) for 1 <= k <= n). %Y A199972 Cf.: A199973 (the sum of LCQ_C(n, k) for 1 <= k <= n). %K A199972 nonn %O A199972 1,3 %A A199972 _Jaroslav Krizek_, Nov 26 2011