cp's OEIS Frontend

A109425 Numbers k such that tau(k)/omega(k) is an integer, where tau(k) = number of divisors of k and omega(k) = number of distinct prime factors of k.

%I A109425 #14 Sep 29 2024 18:51:59
%S A109425 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A109425 27,28,29,31,32,33,34,35,37,38,39,40,41,43,44,45,46,47,48,49,50,51,52,
%U A109425 53,54,55,56,57,58,59,60,61,62,63,64,65,67,68,69,71,72,73,74,75,76,77,79
%N A109425 Numbers k such that tau(k)/omega(k) is an integer, where tau(k) = number of divisors of k and omega(k) = number of distinct prime factors of k.
%C A109425 Integers greater than 1 and not in A109426.
%H A109425 Amiram Eldar, <a href="/A109425/b109425.txt">Table of n, a(n) for n = 1..10000</a>
%e A109425 The number 12 is 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.
%e A109425 The number 36 is not 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.
%p A109425 with(numtheory): a:=proc(n) if type(tau(n)/nops(factorset(n)), integer)=true then n else fi end: seq(a(n),n=2..90);
%t A109425 f[n_] := DivisorSigma[0, n]/Length[FactorInteger[n]]; Select[ Range[2, 80], IntegerQ[ f[ # ]] &] (* _Robert G. Wilson v_, Jun 30 2005 *)
%t A109425 Select[Range[2,80],IntegerQ[DivisorSigma[0,#]/PrimeNu[#]]&] (* _Harvey P. Dale_, Sep 29 2024 *)
%Y A109425 Complement is A109426.
%Y A109425 Cf. A000005, A001221.
%K A109425 nonn
%O A109425 1,1
%A A109425 _Emeric Deutsch_, Jun 28 2005