cp's OEIS Frontend

A109427 Numbers n such that sigma(n)/omega(n) is an integer [sigma(n) = sum of divisors of n; omega(n) = number of distinct prime factors of n].

%I A109427 #11 Jun 11 2024 10:41:12
%S A109427 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19,20,21,22,23,24,25,26,27,
%T A109427 28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,51,52,
%U A109427 53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,73,74,75,76,77
%N A109427 Numbers n such that sigma(n)/omega(n) is an integer [sigma(n) = sum of divisors of n; omega(n) = number of distinct prime factors of n].
%C A109427 Integers greater than 1 and not in A109428.
%C A109427 What is the density of this sequence? - _Charles R Greathouse IV_, Sep 01 2015
%H A109427 Enrique Pérez Herrero, <a href="/A109427/b109427.txt">Table of n, a(n) for n = 1..10000</a>
%e A109427 The number 12 is in the sequence because sigma(12)=28 (1+2+3+4+6+12) and omega(12)=2 (2,3) and so sigma(12)/omega(12)=14.
%e A109427 The number 36 is not in the sequence because sigma(36)=91 (1+2+3+4+6+9+12+18+36) and omega(36)=2 (2,3) and so sigma(36)/omega(36)=91/2.
%p A109427 with(numtheory): a:=proc(n) if type(sigma(n)/nops(factorset(n)), integer)=true then n else fi end: seq(a(n),n=2..90);
%t A109427 Select[Range[2,80],IntegerQ[DivisorSigma[1,#]/PrimeNu[#]]&] (* _Harvey P. Dale_, Aug 13 2021 *)
%o A109427 (PARI) is(n)=if(n<2, return(0)); my(f=factor(n)); sigma(f)%omega(f)==0 \\ _Charles R Greathouse IV_, Sep 01 2015
%Y A109427 Cf. A109428.
%K A109427 nonn
%O A109427 1,1
%A A109427 _Emeric Deutsch_, Jun 28 2005