OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is 1 - Product_{i>=1} 1-prime(i)^(-1-i) = 0.2789766... - Amiram Eldar, Oct 21 2020
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..5000
EXAMPLE
625 = 5*5*5*5 = prime(3)^4 so it is divisible by prime(3)^(3+1), and thus 625 is included in the sequence.
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(Python)
from sympy import primepi, isprime, primefactors, factorint
def a028234(n):
f=factorint(n)
minf = min(f)
return 1 if n==1 else n//(minf**f[minf])
def a067029(n):
f=factorint(n)
return 0 if n==1 else f[min(f)]
def a049084(n): return primepi(n) if isprime(n) else 0
def a055396(n): return 0 if n==1 else a049084(min(primefactors(n)))
def a(n): return 0 if n==1 else a(a028234(n)) + (1 if a067029(n) > a055396(n) else 0)
print([n for n in range(1, 301) if a(n)!=0]) # Indranil Ghosh, Jun 21 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 18 2016
STATUS
approved