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].
4, 8, 9, 16, 25, 27, 30, 32, 36, 42, 49, 64, 66, 70, 72, 78, 81, 100, 102, 105, 108, 110, 114, 120, 121, 125, 128, 130, 138, 144, 154, 165, 168, 169, 170, 174, 180, 182, 186, 190, 195, 196, 200, 216, 222, 225, 230, 231, 238, 240, 243, 246, 252, 255, 256, 258
Offset: 1
Keywords
Examples
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. 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
Crossrefs
Complement of A109421.
Programs
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Maple
with(numtheory): b:=proc(n) if type(tau(n)/bigomega(n),integer)=false then n else fi end: seq(b(n),n=2..300);
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Mathematica
PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 300], ! IntegerQ[DivisorSigma[0, #]/PrimeOmega[#]] &] (* Jean-François Alcover, May 02 2013 *) Select[Range[2,300],!IntegerQ[DivisorSigma[0,#]/PrimeOmega[#]]&] (* Harvey P. Dale, Jun 11 2022 *)
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