A167185 Largest prime power <= n that is not prime.

1, 1, 1, 4, 4, 4, 4, 8, 9, 9, 9, 9, 9, 9, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 25, 25, 27, 27, 27, 27, 27, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 49, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64

Offset: 1

Author

Michael B. Porter, Oct 29 2009

Keywords

• nonn
• easy

Examples

			For a(14), 10, 12, and 14 are not prime powers, and 11 and 13 are prime powers but they are prime. Since 9 = 3^3 is a prime power, a(14) = 9.
		

Links

• Robert Price, Table of n, a(n) for n = 1..2000

Crossrefs

List of nonprime prime powers: A025475.

Next nonprime prime power: A167184.

Previous prime power including primes: A031218.

Programs

Mathematica

Array[SelectFirst[Range[#, 1, -1], Or[And[! PrimeQ@ #, PrimePowerQ@ #], # == 1] &] &, 74] (* Michael De Vlieger, Jun 14 2017 *)

PARI

isA025475(n) = (omega(n) == 1 & !isprime(n)) || (n == 1)
A167185(n) = {local(m);m=n;while(!isA025475(m),m--);m}

Python

from sympy import factorint
def A167185(n): return next(filter(lambda m:len(f:=factorint(m))<=1 and max(f.values(),default=2)>1, range(n,0,-1))) # Chai Wah Wu, Oct 25 2024

Sage

p = [n for n in (1..81) if (is_prime_power(n) or n == 1) and not is_prime(n)]
r = [[p[i]]*(p[i+1] - p[i]) for i in (0..9)]
print([y for x in r for y in x]) # Peter Luschny, Jun 14 2017