A109428 - OEIS

%I #7 Aug 09 2012 09:03:43

%S 18,36,50,72,84,98,100,144,156,162,196,200,225,228,242,252,273,288,

%T 300,324,336,338,364,372,392,399,400,441,444,468,484,516,525,532,576,

%U 578,624,648,651,676,684,700,722,732,741,756,777,784,800,804,819,868,876

%N Numbers n such that sigma(n)/omega(n) is not 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 A109427.

%H Enrique Pérez Herrero, <a href="/A109428/b109428.txt">Table of n, a(n) for n = 1..5000</a>

%e The number 36 is 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.

%e The number 12 is not 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.

%p with(numtheory): b:=proc(n) if type(sigma(n)/nops(factorset(n)),integer)=false then n else fi end: seq(b(n),n=2..1000);

%t Select[Range[2,1000],!IntegerQ[DivisorSigma[1,#]/PrimeNu[#]]&] (* _Harvey P. Dale_, Aug 09 2012 *)

%Y Cf. A109427.

%K nonn

%O 1,1

%A _Emeric Deutsch_, Jun 28 2005