|
%I #10 Aug 14 2019 15:18:56
%S 2,3,5,6,7,10,11,12,13,14,15,17,18,19,20,21,22,23,24,26,28,29,31,33,
%T 34,35,37,38,39,40,41,43,44,45,46,47,48,50,51,52,53,54,55,56,57,58,59,
%U 60,61,62,63,65,67,68,69,71,73,74,75,76,77,79,80,82,83,84,85,86,87,88,89
%N Numbers n such that tau(n)/bigomega(n) is 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 A109422.
%H Charles R Greathouse IV, <a href="/A109421/b109421.txt">Table of n, a(n) for n = 1..10000</a>
%e 12 is 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.
%e 16 is not 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.
%p with(numtheory): a:=proc(n) if type(tau(n)/bigomega(n),integer)=true then n else fi end: seq(a(n),n=2..110);
%t f[n_] := DivisorSigma[0, n]/Plus @@ Last /@ FactorInteger[n]; Select[ Range[2, 89], IntegerQ[ f[ # ]] &] (* _Robert G. Wilson v_, Jun 29 2005 *)
%t Select[Range[2,100],IntegerQ[DivisorSigma[0,#]/PrimeOmega[#]]&] (* _Harvey P. Dale_, Aug 14 2019 *)
%o (PARI) is(n)=my(f=factor(n)); n>1 && numdiv(f)%vecsum(f[,2])==0 \\ _Charles R Greathouse IV_, Apr 27 2015
%Y Cf. A109422.
%K nonn
%O 1,1
%A _Emeric Deutsch_, Jun 28 2005
|
