A001560 - OEIS

%I M1823 N0724 #39 Dec 23 2021 22:56:45

%S 2,8,9,10,11,15,19,21,22,25,26,27,28,30,31,34,40,42,45,46,47,50,55,57,

%T 58,59,62,64,65,66,70,74,75,78,79,80,84,86,94,96,97,98,100,101,103,

%U 106,108,109,110,112,113,116,117,120,122,124,125,126,128,129,130,131

%N Numbers with an even number of partitions.

%D 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.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001560/b001560.txt">Table of n, a(n) for n = 1..1000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H O. Kolberg, <a href="http://www.mscand.dk/article/view/10584/8605">Note on the parity of the partition function</a>, Math. Scand. 7 1959 377-378. MR0117213 (22 #7995).

%H P. A. MacMahon, <a href="https://doi.org/10.1112/jlms/s1-1.4.225b">The parity of p(n), the number of partitions of n, when n <= 1000</a>, J. London Math. Soc., 1 (1926), 225-226.

%H T. R. Parkin and D. Shanks, <a href="http://www.jstor.org/stable/2003251">On the distribution of parity in the partition function</a>, Math. Comp., 21 (1967), 466-480.

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

%o (PARI) is(n)=numbpart(n)%2==0 \\ _Charles R Greathouse IV_, Apr 08 2015

%Y Cf. A052001, A052002, A000041, A243935.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_