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

12, 18, 20, 28, 44, 45, 48, 50, 52, 60, 63, 68, 72, 75, 76, 80, 84, 90, 92, 98, 99, 108, 112, 116, 117, 120, 124, 126, 132, 140, 147, 148, 150, 153, 156, 162, 164, 168, 171, 172, 175, 176, 180, 188, 192, 198, 200, 204, 207, 208, 212, 220, 228, 234, 236, 242

Offset: 1

Author

Rick L. Shepherd, Apr 11 2002

Keywords

• nonn

Examples

			45 is a term because 45 = 3^2 * 5 gives bigomega(45)=3 and omega(45)=2 and 3/2 is not an integer.
		

Links

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A067340 (complement), A070012 (floor(bigomega(n)/omega(n))).

Different from A084679.

Programs

Mathematica

Select[Range[2,1000],!IntegerQ[PrimeOmega[#]/PrimeNu[#]]&] (* Enrique Pérez Herrero, Dec 20 2012 *)

PARI

v=[]; for(n=2,300,if(denominator(bigomega(n)/omega(n))<>1,v=concat(v,n))); v

PARI

is(n)=my(f=factor(n)[,2]); n>9 && vecsum(f)%#f!=0 \\ Charles R Greathouse IV, Oct 16 2015

Formula

A001222(n)/A001221(n) (i.e. bigomega(n)/omega(n)) is not an integer.