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%I #23 Nov 18 2016 12:55:52
%S 2,22,30,42,490,1002,1958,3010,3718,6842,12310,37338,53174,89134,
%T 105558,124754,204226,614154,1741630,2012558,13848650,34262962,
%U 133230930,214481126,271248950,607163746,4835271870,30388671978,45060624582,88751778802,107438159466
%N Partition numbers (A000041) congruent to 2 (mod 4).
%C Partition numbers having the same number of even divisors as odd divisors.
%C The corresponding indices are in A237280.
%C The intersection of A000041 and A016825.
%H Robert Israel, <a href="/A275029/b275029.txt">Table of n, a(n) for n = 1..500</a>
%e 30 is in the sequence because it is a partition number, and its divisors are [1,2,3,5,6,10,15,30].
%p select(t -> t mod 4 = 2, map(combinat:-numbpart, [$1..500])); # _Robert Israel_, Nov 14 2016
%t Select[PartitionsP@ Range@ 160, Mod[#, 4] == 2 &] (* _Michael De Vlieger_, Nov 15 2016 *)
%o (PARI) a000041(n) = numbpart(n)
%o terms(n) = my(i=0, k=2); while(1, if(Mod(a000041(k), 4)==2, print1(a000041(k), ", "); i++); if(i==n, break); k++)
%o /* Print initial 50 terms as follows */
%o terms(50) \\ _Felix Fröhlich_, Nov 15 2016
%Y Cf. A000041, A016825, A213179, A237280.
%K nonn
%O 1,1
%A _Colin Barker_, Nov 13 2016
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