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 A350032 #18 Jan 11 2022 21:35:35 %S A350032 1,1,1,2,1,2,1,1,3,1,2,5,2,3,1,2,3,1,2,4,1,2,5,1,2,5,1,2,5,1,2,5,1,2, %T A350032 4,1,1,3,7,1,3,6,1,2,5,1,1,4,1,1,3,1,11,2,4,9,2,3,7,1,2,4,7,1,3,6,1,2, %U A350032 4,1,1,3,1,1,2,1,6,1,2,4,1,1,3,3,1,1,1,5,5,1 %N A350032 Write n as n = k1 + k2 + ... + km, so that all k are distinct positive integers and b = A001055(k1) + A001055(k2) + ... + A001055(km) becomes maximal. a(n) is the number of such partitions which attain this maximum. %F A350032 a(n) <= 1 + A066739(n) - A000041(n). %e A350032 a(6) = 2: %e A350032 6 = 1 + 2 + 3 and A001055(1) + A001055(2) + A001055(3) = 3; %e A350032 6 = 2 + 4 and A001055(2) + A001055(4) = 3. %Y A350032 Cf. A000009, A000041, A066739, A001055, A350029. %K A350032 nonn %O A350032 1,4 %A A350032 _Thomas Scheuerle_, Dec 09 2021