cp's OEIS Frontend

A070011 Numbers n such that number of prime factors divided by the number of distinct prime factors is not an integer.

%I A070011 #17 Aug 20 2024 03:22:43
%S A070011 12,18,20,28,44,45,48,50,52,60,63,68,72,75,76,80,84,90,92,98,99,108,
%T A070011 112,116,117,120,124,126,132,140,147,148,150,153,156,162,164,168,171,
%U A070011 172,175,176,180,188,192,198,200,204,207,208,212,220,228,234,236,242
%N A070011 Numbers n such that number of prime factors divided by the number of distinct prime factors is not an integer.
%H A070011 Enrique Pérez Herrero, <a href="/A070011/b070011.txt">Table of n, a(n) for n = 1..5000</a>
%F A070011 A001222(n)/A001221(n) (i.e. bigomega(n)/omega(n)) is not an integer.
%e A070011 45 is a term because 45 = 3^2 * 5 gives bigomega(45)=3 and omega(45)=2 and 3/2 is not an integer.
%t A070011 Select[Range[2,1000],!IntegerQ[PrimeOmega[#]/PrimeNu[#]]&] (* _Enrique Pérez Herrero_, Dec 20 2012 *)
%o A070011 (PARI) v=[]; for(n=2,300,if(denominator(bigomega(n)/omega(n))<>1,v=concat(v,n))); v
%o A070011 (PARI) is(n)=my(f=factor(n)[,2]); n>9 && vecsum(f)%#f!=0 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A070011 Cf. A067340 (complement), A070012 (floor(bigomega(n)/omega(n))).
%Y A070011 Different from A084679.
%K A070011 nonn
%O A070011 1,1
%A A070011 _Rick L. Shepherd_, Apr 11 2002