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%I A001560 M1823 N0724 #39 Dec 23 2021 22:56:45
%S A001560 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 A001560 58,59,62,64,65,66,70,74,75,78,79,80,84,86,94,96,97,98,100,101,103,
%U A001560 106,108,109,110,112,113,116,117,120,122,124,125,126,128,129,130,131
%N A001560 Numbers with an even number of partitions.
%D A001560 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 A001560 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001560 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001560 T. D. Noe, <a href="/A001560/b001560.txt">Table of n, a(n) for n = 1..1000</a>
%H A001560 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 A001560 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 A001560 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 A001560 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 A001560 f[n_, k_] := Select[Range[250], Mod[PartitionsP[#], n] == k &]; Table[f[2, k], {k, 0, 1}] (* _Clark Kimberling_, Jan 05 2014 *)
%o A001560 (PARI) is(n)=numbpart(n)%2==0 \\ _Charles R Greathouse IV_, Apr 08 2015
%Y A001560 Cf. A052001, A052002, A000041, A243935.
%K A001560 nonn,easy
%O A001560 1,1
%A A001560 _N. J. A. Sloane_

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