OFFSET
1,1
COMMENTS
The asymptotic density of this sequence is (6/Pi^2) * Sum_{k>=1} f(a(k)) = 0.0626525..., where f(k) = A112526(k) * Product_{p|k} p/(p+1). - Amiram Eldar, Sep 24 2024
LINKS
EXAMPLE
MATHEMATICA
Select[Range[10^3], !PrimeQ[#] && PrimeQ[p = PrimeOmega[#] - PrimeNu[#]] && OddQ[p] &]
PROG
(PARI) isok(n) = (d=bigomega(n)-omega(n)) && (d != 2) && isprime(d); \\ Michel Marcus, Aug 07 2015
(Python)
from sympy import isprime, primefactors
def omega(n): return 0 if n==1 else len(primefactors(n))
def bigomega(n): return 0 if n==1 else bigomega(n//min(primefactors(n))) + 1
def ok(n):
d = bigomega(n) - omega(n)
return d%2 and isprime(d)
print([n for n in range(1, 1001) if ok(n)]) # Indranil Ghosh, Apr 25 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Carlos Eduardo Olivieri, Aug 06 2015
STATUS
approved