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

1,4

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

List of nonprime prime powers: A025475.

Next nonprime prime power: A167184.

Previous prime power including primes: A031218.

Sequence in context: A120327 A056629 A245356 * A081676 A114555 A361471

Adjacent sequences: A167182 A167183 A167184 * A167186 A167187 A167188

Keyword

nonn,easy

Author

Michael B. Porter, Oct 29 2009

Status

approved