A275029 Partition numbers (A000041) congruent to 2 (mod 4).

2, 22, 30, 42, 490, 1002, 1958, 3010, 3718, 6842, 12310, 37338, 53174, 89134, 105558, 124754, 204226, 614154, 1741630, 2012558, 13848650, 34262962, 133230930, 214481126, 271248950, 607163746, 4835271870, 30388671978, 45060624582, 88751778802, 107438159466

Offset: 1

Author

Colin Barker, Nov 13 2016

Keywords

• nonn

Comments

Partition numbers having the same number of even divisors as odd divisors.

The corresponding indices are in A237280.

The intersection of A000041 and A016825.

Examples

			30 is in the sequence because it is a partition number, and its divisors are [1,2,3,5,6,10,15,30].
		

Links

• Robert Israel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A000041, A016825, A213179, A237280.

Programs

Maple

select(t -> t mod 4 = 2, map(combinat:-numbpart, [$1..500])); # Robert Israel, Nov 14 2016

Mathematica

Select[PartitionsP@ Range@ 160, Mod[#, 4] == 2 &] (* Michael De Vlieger, Nov 15 2016 *)

PARI

a000041(n) = numbpart(n)
terms(n) = my(i=0, k=2); while(1, if(Mod(a000041(k), 4)==2, print1(a000041(k), ", "); i++); if(i==n, break); k++)
/* Print initial 50 terms as follows */
terms(50) \\ Felix Fröhlich, Nov 15 2016