A087173 Smallest prime factor of n-th partition number.

1, 2, 3, 5, 7, 11, 3, 2, 2, 2, 2, 7, 101, 3, 2, 3, 3, 5, 2, 3, 2, 2, 5, 3, 2, 2, 2, 2, 5, 2, 2, 3, 3, 2, 3, 17977, 7, 5, 3, 2, 3, 2, 3, 5, 2, 2, 2, 3, 5, 2, 3, 3, 3, 5, 2, 11, 2, 2, 2, 17, 3, 2, 3, 2, 2, 2, 1181, 3, 5, 2, 3, 11, 23, 2, 2, 7, 10619863, 2, 2, 2, 11, 5, 7, 2, 11, 2, 11, 3, 5, 2473

Offset: 1

Author

Reinhard Zumkeller, Aug 23 2003

Keywords

• nonn

Examples

			A000041(100) = 190569292 = 2*2*43*59*89*211, therefore a(100)=2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Least Prime Factor
• Eric Weisstein's World of Mathematics, Partition Function
• Eric Weisstein's World of Mathematics, Partition Function P Congruences

Crossrefs

Cf. A071963.

Programs

Mathematica

FactorInteger[#][[1,1]]&/@PartitionsP[Range[90]] (* Harvey P. Dale, May 20 2023 *)

PARI

spf(n) = if (n==1, 1, vecmin(factor(n)[,1]));
a(n) = spf(numbpart(n)); \\ Michel Marcus, Feb 24 2023

Formula

a(n) = A020639(A000041(n)).