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A001560
Numbers with an even number of partitions.
(Formerly M1823 N0724)
12
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
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
KEYWORD
nonn,easy
STATUS
approved