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%I #9 Aug 13 2021 15:54:35
%S 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 28,29,30,31,32,33,34,35,37,38,39,40,41,42,43,44,45,46,47,48,49,51,52,
%U 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 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 Integers greater than 1 and not in A109428.
%C What is the density of this sequence? - _Charles R Greathouse IV_, Sep 01 2015
%H Enrique Pérez Herrero, <a href="/A109427/b109427.txt">Table of n, a(n) for n = 1..10000</a>
%e 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 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 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 Select[Range[2,80],IntegerQ[DivisorSigma[1,#]/PrimeNu[#]]&] (* _Harvey P. Dale_, Aug 13 2021 *)
%o (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 Cf. A109428.
%K nonn
%O 1,1
%A _Emeric Deutsch_, Jun 28 2005
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