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

1,6

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A014673, A020639, A028234, A292269.

Sequence in context: A340084 A317939 A086767 * A226040 A302034 A302044

Adjacent sequences: A119285 A119286 A119287 * A119289 A119290 A119291

Keyword

nonn

Author

Reinhard Zumkeller, May 13 2006

Extensions

Name changed by Antti Karttunen, Oct 04 2017

Status

approved