cp's OEIS Frontend

A109423 Numbers n such that sigma(n)/bigomega(n) is an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].

%I A109423 #13 Jan 17 2017 02:33:35
%S A109423 2,3,5,6,7,8,10,11,13,14,15,17,18,19,20,21,22,23,24,26,29,30,31,33,34,
%T A109423 35,37,38,39,41,42,43,44,45,46,47,50,51,53,54,55,56,57,58,59,60,61,62,
%U A109423 65,66,67,68,69,70,71,72,73,74,77,78,79,82,83,84,85,86,87,88,89,91,92
%N A109423 Numbers n such that sigma(n)/bigomega(n) is an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].
%C A109423 Integers greater than 1 and not in A109424.
%C A109423 Contains all primes and squarefree semiprimes (A006881). - _Robert Israel_, Jan 16 2017
%H A109423 Robert Israel, <a href="/A109423/b109423.txt">Table of n, a(n) for n = 1..10000</a>
%e A109423 The number 24 is in the sequence because sigma(24)=60 (1+2+3+4+6+8+12+24) and bigomega(24)=4 (2,2,2,3) and so sigma(24)/bigomega(24) = 15.
%e A109423 The number 12 is not in the sequence because sigma(12)=28 (1+2+3+4+6+12) and bigomega(12)=3 (2,2,3) and so sigma(12)/bigomega(12) = 28/3.
%p A109423 with(numtheory): a:=proc(n) if type(sigma(n)/bigomega(n),integer)=true then n else fi end: seq(a(n),n=2..110);
%t A109423 PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 100], IntegerQ[DivisorSigma[1, #]/PrimeOmega[#]] &] (* _Jean-François Alcover_, May 02 2013 *)
%o A109423 (PARI) isok(n) = denominator(sigma(n)/bigomega(n)) == 1; \\ _Michel Marcus_, Jan 17 2017
%Y A109423 Cf. A006881, A109424.
%K A109423 nonn
%O A109423 1,1
%A A109423 _Emeric Deutsch_, Jun 28 2005