cp's OEIS Frontend

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].

%I A109422 #7 Jun 11 2022 15:15:15
%S A109422 4,8,9,16,25,27,30,32,36,42,49,64,66,70,72,78,81,100,102,105,108,110,
%T A109422 114,120,121,125,128,130,138,144,154,165,168,169,170,174,180,182,186,
%U A109422 190,195,196,200,216,222,225,230,231,238,240,243,246,252,255,256,258
%N 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].
%C A109422 Integers greater than 1 and not in A109421.
%e A109422 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 A109422 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 A109422 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 A109422 PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 300], ! IntegerQ[DivisorSigma[0, #]/PrimeOmega[#]] &] (* _Jean-François Alcover_, May 02 2013 *)
%t A109422 Select[Range[2,300],!IntegerQ[DivisorSigma[0,#]/PrimeOmega[#]]&] (* _Harvey P. Dale_, Jun 11 2022 *)
%Y A109422 Complement of A109421.
%K A109422 nonn
%O A109422 1,1
%A A109422 _Emeric Deutsch_, Jun 28 2005