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A088530 Denominator of Bigomega(n)/Omega(n). 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,11

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..10000

Index entries for sequences computed from exponents in factorization of n

FORMULA

Let B = number of prime divisors of n with multiplicity, O = number of distinct prime divisors of n. Then a(n) = denominator of B/O.

EXAMPLE

a(4!) = bigomega(4!) / omega(4!) = 4/2 = 2/1

MATHEMATICA

Table[Denominator[PrimeOmega[n]/PrimeNu[n]], {n, 2, 100}] (* Harvey P. Dale, Mar 22 2012 *)

PROG

(PARI) for(x=2, 100, y=bigomega(x)/omega(x); print1(denominator(y)", "))

(Python)

from sympy import primefactors

from fractions import Fraction

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 Fraction(str(bigomega(n)) + '/' + str(omega(n))).denominator

print map(a, xrange(2, 151)) # Indranil Ghosh, Jul 13 2017

CROSSREFS

Cf. A070012, A070013, A070014, A088529 (gives the numerator).

Sequence in context: A124148 A174435 A294883 * A058060 A088323 A003652

Adjacent sequences:  A088527 A088528 A088529 * A088531 A088532 A088533

KEYWORD

nonn,frac

AUTHOR

Cino Hilliard, Nov 16 2003

STATUS

approved

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Last modified November 12 19:33 EST 2019. Contains 329078 sequences. (Running on oeis4.)