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 A109422 Numbers n such that tau(n)/bigomega(n) is not an integer [tau(n) =number of divisors of n; bigomega(n)=number of prime divisors of n, counted with multiplicities]. 1

%I

%S 4,8,9,16,25,27,30,32,36,42,49,64,66,70,72,78,81,100,102,105,108,110,

%T 114,120,121,125,128,130,138,144,154,165,168,169,170,174,180,182,186,

%U 190,195,196,200,216,222,225,230,231,238,240,243,246,252,255,256,258

%N Numbers n such that tau(n)/bigomega(n) is not an integer [tau(n) =number of divisors of n; bigomega(n)=number of prime divisors of n, counted with multiplicities].

%C Integers greater than 1 and not in A109421.

%e 16 is in the sequence because tau(16)=5 (1,2,4,8,16) and bigomega(16)=4 (2,2,2,2) and so tau(16)/bigomega(16)=5/4.

%e 12 is not in the sequence because tau(12)=6 (1,2,3,4,6,12) and bigomega(12)=3 (2,2,3) and so tau(12)/bigomega(12)=2

%p with(numtheory): b:=proc(n) if type(tau(n)/bigomega(n),integer)=false then n else fi end: seq(b(n),n=2..300);

%t PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 300], ! IntegerQ[DivisorSigma[0, #]/PrimeOmega[#]] &] (* _Jean-François Alcover_, May 02 2013 *)

%Y Complement of A109421.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Jun 28 2005

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Last modified July 30 15:29 EDT 2021. Contains 346359 sequences. (Running on oeis4.)