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A088530
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Denominator of bigomega(n)/omega(n).
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27
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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
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OFFSET
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2,11
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COMMENTS
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LINKS
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FORMULA
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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.
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EXAMPLE
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bigomega(24) / omega(24) = 4/2 = 2/1, so a(24) = 1.
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MAPLE
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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
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MATHEMATICA
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Table[Denominator[PrimeOmega[n]/PrimeNu[n]], {n, 2, 100}] (* Harvey P. Dale, Mar 22 2012 *)
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PROG
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(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()
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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