A049575 Prime partition numbers.

2, 3, 5, 7, 11, 101, 17977, 10619863, 6620830889, 80630964769, 228204732751, 1171432692373, 1398341745571, 10963707205259, 15285151248481, 10657331232548839, 790738119649411319, 18987964267331664557, 74878248419470886233, 1394313503224447816939

Offset: 1

Author

G. L. Honaker, Jr.

Keywords

• nonn
• nice

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..100
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• G. K. Patil, Ramanujan's Life And His Contributions In The Field Of Mathematics, International Journal of Scientific Research and Engineering Studies (IJSRES), 1(6) (2014), ISSN: 2349-8862.
• Eric Weisstein's World of Mathematics, Partition Function P Congruences.
• Eric Weisstein's World of Mathematics, Partition Function P.

Crossrefs

Intersection of A000040 and A000041.

Cf. A046063, A051143.

Cf. A038753, A065728. - Reinhard Zumkeller, Nov 03 2009

Programs

Mathematica

lst={};Do[a=PartitionsP[n];If[PrimeQ[a],AppendTo[lst,a]],{n,2*6!}];lst (* Vladimir Joseph Stephan Orlovsky, Jun 14 2009 *)
Select[PartitionsP[Range[1000]],PrimeQ] (* Harvey P. Dale, Mar 11 2013 *)

PARI

for(n=0,10^3,my(p=numbpart(n));if(isprime(p),print1(p,", "))); \\ Joerg Arndt, May 09 2013

Formula

a(n) = A000041(A046063(n)) = A000040(A051143(n)). - M. F. Hasler, Oct 19 2008

A010051(a(n))*A167392(a(n)) = 1. - Reinhard Zumkeller, Nov 03 2009

Extensions

More terms from James Sellers and Christian G. Bower, Oct 15 1999.