A070011 - OEIS

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

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OFFSET

1,1

LINKS

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

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

PROG

(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

CROSSREFS

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

Different from A084679.

Sequence in context: A162947 A351201 A359892 * A084679 A072588 A267117

Adjacent sequences: A070008 A070009 A070010 * A070012 A070013 A070014

KEYWORD

nonn

AUTHOR

Rick L. Shepherd, Apr 11 2002

STATUS

approved