A065728 -id:A065728 - 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.

A065729 Numbers k such that the k-th partition number (A000041(k)) is a semiprime.

Original entry on oeis.org

7, 8, 12, 23, 65, 67, 76, 81, 87, 90, 92, 93, 95, 121, 123, 143, 146, 161, 181, 203, 218, 220, 235, 241, 251, 252, 287, 321, 330, 388, 406, 423, 437, 438, 443, 455, 456, 507, 555, 594, 603, 626, 646, 661, 665, 672, 685, 707, 708, 715, 720, 755, 808, 837, 856

Offset: 1

Patrick De Geest, Nov 18 2001

nonn

			The 808th partition number 8151756509675604512522473567 = 5963320232189 * 1366982853893003.

Harry J. Smith, Table of n, a(n) for n = 1..100
Hisanori Mishima, Factorization results
Eric Weisstein's World of Mathematics, Semiprime.

Cf. A000041, A001358, A049575, A065728.

Select[Range[900],PrimeOmega[PartitionsP[#]]==2&] (* Harvey P. Dale, Nov 27 2024 *)

isok(k) = { bigomega(numbpart(k))==2 } \\ Harry J. Smith, Oct 28 2009

Offset changed from 0 to 1 by Harry J. Smith, Oct 28 2009

Missing a(38) = 507 added by Harry J. Smith, Oct 28 2009

A121061 Numbers k such that k-th partition number A000041(k) is a 3-almost prime (A014612).

Original entry on oeis.org

9, 10, 16, 18, 20, 22, 25, 29, 31, 34, 37, 42, 45, 48, 50, 56, 57, 60, 63, 69, 71, 72, 73, 83, 85, 91, 101, 102, 112, 113, 114, 119, 139, 144, 148, 151, 155, 156, 172, 175, 183, 185, 190, 192, 195, 202, 208, 217, 238, 242, 244, 245, 247, 256, 257, 272, 275, 291, 293

Offset: 1

Jonathan Vos Post, Aug 09 2006

			a(1) = 9 because P(9) = 30 = 2 * 3 * 5.
a(2) = 10 because P(10) = 42 = 2 * 3 * 7.
a(3) = 16 because P(16) = 231 = 3 * 7 * 11.

Cf. A000041, A046063, A065728, A065729.

Select[Range[300],PrimeOmega[PartitionsP[#]]==3&] (* James C. McMahon, Oct 12 2024 *)

A000041(a(n)) in A014612.

112 and 113 inserted by R. J. Mathar, Dec 22 2010

cp's OEIS Frontend

A049575 Prime partition numbers.

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A065729 Numbers k such that the k-th partition number (A000041(k)) is a semiprime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A121061 Numbers k such that k-th partition number A000041(k) is a 3-almost prime (A014612).

Views

Author

Keywords

Examples

Crossrefs

Programs

Mathematica

Formula

Extensions