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 A306631 #16 Feb 16 2025 08:33:55
%S A306631 1,2,3,3,4,4,5,5,5,6,6,6,6,6,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,9,9,9,9,9,
%T A306631 9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,
%U A306631 11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12
%N A306631 Inverse of the Hardy-Ramanujan asymptotic partition function.
%H A306631 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>
%H A306631 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_function_(number_theory)">Partition function</a>
%F A306631 a(n) = 6*LambertW(-1, -Pi/(2*sqrt(2)*3^(3/4)*sqrt(n)))^2/Pi^2 rounded to the nearest integer.
%F A306631 Conjecture: a(A000041(n)) = n for all n > 9.
%e A306631 A000041(10) = 42, then a(42) = 10.
%t A306631 a[n_] := 6*ProductLog[-1, -Pi/(2*Sqrt[2]*3^(3/4)*Sqrt[n])]^2/Pi^2 // Round;
%t A306631 Table[a[n], {n, 2, 100}]
%Y A306631 Cf. A000041, A050811.
%K A306631 nonn
%O A306631 2,2
%A A306631 _Jean-François Alcover_, Mar 02 2019