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 A345129 #3 Jun 08 2021 21:16:54
%S A345129 0,1,2,3,6,5,16,22,14,21,40,46,94,46,40,109,208,159,182,161,148,268,
%T A345129 296,380,380,472,488,497,770,620,666,851,740,1082,560,1015,1506,1226,
%U A345129 946,1490,2088,1381,2566,1941,2160,2379,2832,2489,2976,3111,2290,3832,4732,3395,3340
%N A345129 Sum of the squarefree products s*t from all positive integer pairs (s,t), such that s + t = n, s <= t.
%F A345129 a(n) = Sum_{k=1..floor(n/2)} k * (n-k) * mu(k*(n-k))^2, where mu is the Möbius function (A008683).
%e A345129 a(13) = 94; The partitions of 13 into two positive integer parts (s,t) where s <= t are (1,12), (2,11), (3,10), (4,9), (5,8), (6,7). The corresponding products are 1*12, 2*11, 3*10, 4*9, 5*8, and 6*7. The sum of the squarefree products from this list is 22 + 30 + 42 = 94.
%t A345129 Table[Sum[k (n - k) MoebiusMu[k (n - k)]^2, {k, Floor[n/2]}], {n, 80}]
%Y A345129 Cf. A008683 (mu), A325148.
%K A345129 nonn
%O A345129 1,3
%A A345129 _Wesley Ivan Hurt_, Jun 08 2021