A213179 -id:A213179 - cp's OEIS frontend

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

Colin Barker, Nov 13 2016

nonn

Partition numbers having the same number of even divisors as odd divisors.
The corresponding indices are in A237280.
The intersection of A000041 and A016825.

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

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

Cf. A000041, A016825, A213179, A237280.

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

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

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

A235704 a(n) is the smallest number k such that n*k is a partition number.

Original entry on oeis.org

1, 1, 1, 14, 1, 5, 1, 7, 15, 3, 1, 66, 286, 3, 1, 11, 22715, 44, 33, 35761, 2, 1, 363, 33, 63, 143, 5, 2, 84, 1, 2425, 72610, 7, 2725580, 11, 22, 926026, 3283, 123981330, 58088, 363, 1, 70, 4, 3, 176484, 11209, 85166, 10, 141790, 11209835405

Offset: 1

Omar E. Pol, Jan 14 2014

nonn

			For n = 4, a(4) = 14 because if 1 <= k <= 13 we have that 4*k is not a partition number, but if k = 14 then 4*14 = 56 and 56 is the number of partitions of 11.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000041, A046641, A072871, A213179, A213365, A216258, A217725, A217726, A222175, A222178, A222179, A225317, A225361.

a[n_] := PartitionsP[NestWhile[(# + 1)&, 1, Mod[PartitionsP@ #, n] > 0 &]]/n; Array[a,51] (* Giovanni Resta, Jan 15 2014 *)

a(n) = 1 iff n is a partition number.

a(n) = A072871(n)/n.

cp's OEIS Frontend

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

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