A038753 -id:A038753 - cp's OEIS frontend

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

G. L. Honaker, Jr.

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.

Intersection of A000040 and A000041.
Cf. A046063, A051143.
Cf. A038753, A065728. - Reinhard Zumkeller, Nov 03 2009

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 *)

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

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

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

A236107 Nonprimes whose divisors are partition numbers.

Original entry on oeis.org

1, 15, 22, 77

Offset: 1

Omar E. Pol, Jan 22 2014

By definition all terms are partition numbers.

Conjecture: no terms exist beyond 77. - Jon E. Schoenfield, Feb 05 2014

			15 is in the sequence because 15 is a nonprime number and the divisors of 15 are 1, 3, 5, 15, which are also partition numbers.

Cf. A000041, A018252, A038753, A236102, A236103, A236105, A236108, A236110.

nmax = 1000;
pp = PartitionsP[Range[nmax]];
selQ[n_] := Module[{dd = Divisors[n]}, Intersection[pp, dd] == dd];
Select[Range[nmax], !PrimeQ[#] && selQ[#]&] (* Jean-François Alcover, Apr 09 2020 *)

cp's OEIS Frontend

A049575 Prime partition numbers.

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