1,1

Let d(k, m) be the asymptotic density of k-free numbers (numbers not divisible by a k-th power of a prime) that are not divisible by the first m primes. Then, d(k, m) = (1/zeta(k)) * Product_{j=1..m} (1-1/prime(j))/(1-1/prime(j)^k). The asymptotic density of terms whose smallest prime divisor is prime(i) is delta(i) = d(prime(i)+1, i-1) - d(prime(i), i-1) - d(prime(i)+1, i) + d(prime(i), i) and the asymptotic density of this sequence is Sum_{i>=1} delta(i) = 0.16785889468250175464... . - Amiram Eldar, Jun 24 2022

Harvey P. Dale, Table of n, a(n) for n = 1..1000

126 = 2 * 3^2 * 7 minimum prime is 2, largest exponent is also 2, hence 126 is in the sequence.

spleQ[n_]:=Module[{f=FactorInteger[n]}, f[[1, 1]]==Max[f[[All, 2]]]]; Select[ Range[2, 400], spleQ] (* Harvey P. Dale, Aug 19 2017 *)

(Python)

from sympy import factorint

def aupto(limit):

alst = []

for k in range(4, limit+1):

f = factorint(k)

if min(f) == max(f[p] for p in f): alst.append(k)

return alst

print(aupto(338)) # Michael S. Branicky, Apr 12 2021

Subsequence of A111371.

Sequence in context: A362873 A111371 A389216 * A324519 A381953 A230628

Adjacent sequences: A078511 A078512 A078513 * A078515 A078516 A078517

Benoit Cloitre, Jan 06 2003

approved