A001560 Numbers with an even number of partitions. (Formerly M1823 N0724)

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

1,1

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A052001, A052002, A000041, A243935.

Sequence in context: A237415 A247635 A152754 * A175463 A356061 A167450

Adjacent sequences: A001557 A001558 A001559 * A001561 A001562 A001563

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved