A088530 - OEIS

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A088530

Denominator of bigomega(n)/omega(n).

27

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

COMMENTS

a(n) is the denominator of A022559(n)/A000720(n). - Robert Israel, Jan 08 2024

LINKS

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

R. L. Duncan, On the factorization of integers, Proc. Amer. Math. Soc. 25 (1970), 191-192.

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

bigomega(24) / omega(24) = 4/2 = 2/1, so a(24) = 1.

MAPLE

N:= 100:

W:= ListTools:-PartialSums(map(numtheory:-bigomega, [$1..N])):

seq(denom(W[i]/numtheory:-pi(i)), i=2..N); # Robert Israel, Jan 08 2024

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, Integer

def bigomega(n): return 0 if n==1 else bigomega(Integer(n)/primefactors(n)[0]) + 1

def omega(n): return Integer(len(primefactors(n)))

def a(n): return (bigomega(n)/omega(n)).denominator()

print([a(n) for n in range(2, 51)]) # Indranil Ghosh, Jul 13 2017

CROSSREFS

Cf. A001221, A001222, A000720, A022559, A070012, A070013, A070014, A088529 (gives the numerator).

Sequence in context: A330749 A294883 A348940 * A058060 A338160 A336137

Adjacent sequences: A088527 A088528 A088529 * A088531 A088532 A088533

KEYWORD

nonn,frac,look

AUTHOR

Cino Hilliard, Nov 16 2003

STATUS

approved