A119288 a(n) is the second smallest prime factor of n, or 1 if n is a prime power.

1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 3, 1, 5, 7, 11, 1, 3, 1, 13, 1, 7, 1, 3, 1, 1, 11, 17, 7, 3, 1, 19, 13, 5, 1, 3, 1, 11, 5, 23, 1, 3, 1, 5, 17, 13, 1, 3, 11, 7, 19, 29, 1, 3, 1, 31, 7, 1, 13, 3, 1, 17, 23, 5, 1, 3, 1, 37, 5, 19, 11, 3, 1, 5, 1, 41, 1, 3, 17, 43, 29, 11, 1, 3, 13, 23

Offset: 1

Author

Reinhard Zumkeller, May 13 2006

Keywords

• nonn

Comments

Least prime factor of {n divided by the maximal power of the least prime factor of n}. - after the original name of the sequence.

a(n) = A020639(A028234(n)).

a(n) = 1 iff n is a prime power: a(A000961(n))=1 and a(A024619(n))>1.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014673, A020639, A028234, A292269.

Programs

Mathematica

Join[{1},Table[Which[PrimePowerQ[n],1,True,FactorInteger[n][[2,1]]],{n,2,100}]] (* Harvey P. Dale, Feb 08 2020 *)

PARI

a(n) = if (isprimepower(n) || (n==1), 1, my(f=factor(n)[,1]); f[2]); \\ Michel Marcus, Mar 01 2023

Python

from sympy import primefactors
def A119288(n): return 1 if len(s:=primefactors(n)) <= 1 else sorted(s)[1] # Chai Wah Wu, Mar 31 2023

Formula

A010055(n) = 0^(a(n)-1). - Reinhard Zumkeller, May 13 2006

Extensions

Name changed by Antti Karttunen, Oct 04 2017