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

1,2

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A071963.

Sequence in context: A194261 A194262 A039710 * A179335 A330994 A097858

Adjacent sequences: A087170 A087171 A087172 * A087174 A087175 A087176

Keyword

nonn

Author

Reinhard Zumkeller, Aug 23 2003

Status

approved