A036042 k appears partition(k) times.

0, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 1972, p. 831, column labeled "n".

Links

• Robert Price, Table of n, a(n) for n = 0..9295 (0 <= k <=25).
• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Crossrefs

Cf. A000041, A052002.

Programs

Mathematica

Table[ConstantArray[n, PartitionsP[n]], {n, 0, 9}] // Flatten  (* Robert Price, Jun 12 2020 *)

Formula

Sum_{n>=1} (-1)^(n+1)/a(n) = Sum_{n>=2} (-1)^n/A052002(n) = 0.78686... . - Amiram Eldar, Feb 18 2024