A049575 - OEIS

A049575

Prime partition numbers.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

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

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 *)

PROG

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

CROSSREFS

Intersection of A000040 and A000041.