cp's OEIS Frontend

A109426 Numbers n such that tau(n)/omega(n) is not an integer [tau(n) =number of divisors of n; omega(n)=number of distinct prime factors of n].

%I A109426 #13 Oct 03 2015 14:23:54
%S A109426 30,36,42,66,70,78,100,102,105,110,114,120,130,138,144,154,165,168,
%T A109426 170,174,182,186,190,195,196,222,225,230,231,238,240,246,255,258,264,
%U A109426 266,270,273,280,282,285,286,290,310,312,318,322,324,336,345,354,357,366
%N A109426 Numbers n such that tau(n)/omega(n) is not an integer [tau(n) =number of divisors of n; omega(n)=number of distinct prime factors of n].
%C A109426 Integers greater than 1 and not in A109425.
%H A109426 Enrique Pérez Herrero, <a href="/A109426/b109426.txt">Table of n, a(n) for n = 1..10000</a>
%e A109426 The number 36 is in the sequence because tau(36)=9 (1,2,3,4,6,9,12,18,36) and omega(36)=2 (2,3) and so tau(36)/omega(36)=9/2.
%e A109426 The number 12 is not in the sequence because tau(12)=6 (1,2,3,4,6,12) and omega(12)=2 (2,3) and so tau(12)/omega(12)=3.
%p A109426 with(numtheory): b:=proc(n) if type(tau(n)/nops(factorset(n)),integer)=false then n else fi end: seq(b(n),n=2..400);
%t A109426 f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 369], !IntegerQ[ f[ # ]] &] (* _Robert G. Wilson v_, Jun 30 2005 *)
%t A109426 Select[Range[2,400],!IntegerQ[DivisorSigma[0,#]/PrimeNu[#]]&] (* _Harvey P. Dale_, Oct 03 2015 *)
%o A109426 (PARI) is(n)=numdiv(n)%omega(n)>0 \\ _Charles R Greathouse IV_, May 15 2013
%Y A109426 Complement is A109425.
%K A109426 nonn
%O A109426 1,1
%A A109426 _Emeric Deutsch_, Jun 28 2005