A306631 Inverse of the Hardy-Ramanujan asymptotic partition function.

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, 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, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12

Offset: 2

Author

Jean-François Alcover, Mar 02 2019

Keywords

• nonn

Examples

			A000041(10) = 42, then a(42) = 10.
		

Links

• Eric Weisstein's MathWorld, Partition Function P
• Wikipedia, Partition function

Crossrefs

Cf. A000041, A050811.

Programs

Mathematica

a[n_] := 6*ProductLog[-1, -Pi/(2*Sqrt[2]*3^(3/4)*Sqrt[n])]^2/Pi^2 // Round;
Table[a[n], {n, 2, 100}]

Formula

a(n) = 6*LambertW(-1, -Pi/(2*sqrt(2)*3^(3/4)*sqrt(n)))^2/Pi^2 rounded to the nearest integer.

Conjecture: a(A000041(n)) = n for all n > 9.