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 A245803 Numerator of the partial sum of the number of prime factors function divided by n. 0

%I

%S 0,1,2,1,1,7,8,11,13,3,16,19,20,11,8,7,29,16,33,9,38,20,41,15,47,49,

%T 52,55,56,59,60,65,67,69,71,25,76,39,80,21,85,44,89,23,19,97,98,103,

%U 15,54,110,113,114,59,24,31,42,64,129,133,134,68,139,145,147,25,151,77,52,159,160,55

%N Numerator of the partial sum of the number of prime factors function divided by n.

%F a(n) is the numerator of (sum(i = 1 .. n, Omega(i)))/n, where Omega is the number of prime factors function (counted with multiplicity, see A001222).

%e a(8) = 11, since the integers from 1 to 8 have between them a total of 11 prime factors, making our fraction here 11/8.

%e a(9) = 13, since the integers from 1 to 9 have between them a total of 13 prime factors, making our fraction here 13/9.

%e a(10) = 3, since the integers from 1 to 10 have between them a total of 15 prime factors, making our fraction here 15/10 = 3/2.

%p N:= 100: # to get terms a(1) to a(N)

%p map(numer, zip(`/`,ListTools:-PartialSums([seq(numtheory:-bigomega(n),n=1..N)]),[\$1..N])); # _Robert Israel_, Aug 29 2014

%t Numerator[Array[Plus@@Last/@FactorInteger[#!] &, 120, 2]/Range[2, 121]]

%o (PARI) lista(nn) = {s = 0; for (n=1, nn, s += bigomega(n); print1(numerator(s/n), ", "););} \\ _Michel Marcus_, Aug 28 2014

%Y Cf. A022559.

%K nonn,easy,frac

%O 1,3

%A _Alonso del Arte_, Aug 22 2014

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Last modified June 12 23:10 EDT 2021. Contains 344978 sequences. (Running on oeis4.)