A052003 Odd partition numbers.

1, 3, 5, 7, 11, 15, 77, 101, 135, 231, 297, 385, 627, 1255, 1575, 4565, 8349, 10143, 14883, 17977, 21637, 26015, 31185, 44583, 63261, 75175, 147273, 173525, 239943, 281589, 329931, 386155, 526823, 966467, 1121505, 1505499, 2679689, 3087735

Offset: 1

Author

Patrick De Geest, Nov 15 1999

Keywords

• nonn

Comments

Intersection of A005408 and A000041; A000035(a(n))*A167392(a(n)) = 1; a(n) = A000041(A052002(n+1)). - Reinhard Zumkeller, Nov 03 2015

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..1000 (terms 1..529 from G. C. Gruebel).
• K. Ono, Odd values of the partition function
• K. Ono, Odd values of the partition function, Discrete Mathematics 169, 1997, pp. 263-268.

Crossrefs

Cf. A052002, A000041.

Programs

Haskell

a052003 n = a052003_list !! n
a052003_list = filter odd a000041_list
-- Reinhard Zumkeller, Nov 03 2015

Maple

select(type, [seq(combinat:-numbpart(n),n=1..200)],odd); # Robert Israel, Nov 03 2015

Mathematica

Select[PartitionsP[Range[50]], OddQ] (* Vladimir Reshetnikov, Nov 02 2015 *)

PARI

for(n=1, 100, if((k=numbpart(n))%2==1, print1(k", "))) \\ Altug Alkan, Nov 02 2015