cp's OEIS Frontend

A109424 Numbers n such that sigma(n)/bigomega(n) is not an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].

%I A109424 #19 Aug 12 2020 13:47:30
%S A109424 4,9,12,16,25,27,28,32,36,40,48,49,52,63,64,75,76,80,81,90,100,104,
%T A109424 112,117,121,124,128,136,144,148,162,169,171,172,175,176,180,192,196,
%U A109424 208,225,232,234,243,244,252,256,268,272,273,279,289,292,296,300,306,316
%N A109424 Numbers n such that sigma(n)/bigomega(n) is not an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].
%C A109424 Integers greater than 1 and not in A109423.
%C A109424 Includes all squares > 1. - _Robert Israel_, Jan 16 2017
%H A109424 Robert Israel, <a href="/A109424/b109424.txt">Table of n, a(n) for n = 1..10000</a>
%e A109424 The number 12 is 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.
%e A109424 The number 24 is not 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.
%p A109424 with(numtheory): b:=proc(n) if type(sigma(n)/bigomega(n),integer)=false then n else fi end: seq(b(n),n=2..340);
%t A109424 PrimeOmega[n_] := Plus @@ FactorInteger[n][[All, 2]]; Select[Range[2, 320], ! IntegerQ[DivisorSigma[1, #]/PrimeOmega[#]] &] (* _Jean-François Alcover_, May 02 2013 *)
%t A109424 Select[Range[2,320],!IntegerQ[DivisorSigma[1,#]/PrimeOmega[#]]&] (* _Harvey P. Dale_, Aug 12 2020 *)
%o A109424 (PARI) isok(n) = denominator(sigma(n)/bigomega(n)) != 1; \\ _Michel Marcus_, Jan 17 2017
%Y A109424 Cf. A000290, A109423.
%K A109424 nonn
%O A109424 1,1
%A A109424 _Emeric Deutsch_, Jun 28 2005