OFFSET
2,3
COMMENTS
a(n) is the ceiling of the average of the exponents in the prime factorization of n.
LINKS
FORMULA
a(n) = ceiling(bigomega(n)/omega(n)) for n>=2.
EXAMPLE
a(12) = 2 because 12 = 2^2 * 3^1 and ceiling(bigomega(12)/omega(12)) = ceiling((2+1)/2) = 2. a(36) = 2 because 36 = 2^2 * 3^2 and ceiling(bigomega(36)/omega(36)) = ceiling((2+2)/2) = 2. a(60) = 2 because 60 = 2^2 * 3^1 * 5^1 and ceiling(bigomega(60)/omega(60)) = ceiling((2+1+1)/3) = 2. 36 is in A067340. 12 and 60 are in A070011.
MATHEMATICA
Table[Ceiling[PrimeOmega[n]/PrimeNu[n]], {n, 2, 106}] (* Michael De Vlieger, Jul 12 2017 *)
PROG
(PARI) v=[]; for(n=2, 150, v=concat(v, ceil(bigomega(n)/omega(n)))); v
(Scheme) (define (A070014 n) (let ((a (A001222 n)) (b (A001221 n))) (if (zero? (modulo a b)) (/ a b) (+ 1 (/ (- a (modulo a b)) b))))) ;; Antti Karttunen, Jul 12 2017
(Python)
from sympy import primefactors, ceiling
def bigomega(n): return 0 if n==1 else bigomega(n//primefactors(n)[0]) + 1
def omega(n): return len(primefactors(n))
def a(n): return ceiling(bigomega(n)/omega(n))
print([a(n) for n in range(2, 51)]) # Indranil Ghosh, Jul 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Apr 11 2002
STATUS
approved