A001560 Numbers with an even number of partitions.

2, 8, 9, 10, 11, 15, 19, 21, 22, 25, 26, 27, 28, 30, 31, 34, 40, 42, 45, 46, 47, 50, 55, 57, 58, 59, 62, 64, 65, 66, 70, 74, 75, 78, 79, 80, 84, 86, 94, 96, 97, 98, 100, 101, 103, 106, 108, 109, 110, 112, 113, 116, 117, 120, 122, 124, 125, 126, 128, 129, 130, 131

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 836.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• 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].
• O. Kolberg, Note on the parity of the partition function, Math. Scand. 7 1959 377-378. MR0117213 (22 #7995).
• P. A. MacMahon, The parity of p(n), the number of partitions of n, when n <= 1000, J. London Math. Soc., 1 (1926), 225-226.
• T. R. Parkin and D. Shanks, On the distribution of parity in the partition function, Math. Comp., 21 (1967), 466-480.

Crossrefs

Cf. A052001, A052002, A000041, A243935.

Programs

Mathematica

f[n_, k_] := Select[Range[250], Mod[PartitionsP[#], n] == k &]; Table[f[2, k], {k, 0, 1}] (* Clark Kimberling, Jan 05 2014 *)

PARI

is(n)=numbpart(n)%2==0 \\ Charles R Greathouse IV, Apr 08 2015