A134334 Numbers which are not divisible by the number of their prime factors (counted with multiplicity).

8, 9, 15, 20, 21, 25, 28, 32, 33, 35, 39, 44, 48, 49, 50, 51, 52, 54, 55, 57, 64, 65, 68, 69, 70, 72, 76, 77, 81, 85, 87, 90, 91, 92, 93, 95, 98, 108, 110, 111, 112, 115, 116, 119, 121, 123, 124, 125, 126, 128, 129, 130, 133, 135, 141, 143, 145, 148, 150, 154, 155, 159

Offset: 1

Author

Hieronymus Fischer, Oct 23 2007

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1 (Erdős and Pomerance, 1990). - Amiram Eldar, Jul 10 2020

Examples

			a(1) = 8, since 8 = 2*2*2 has 3 prime factors and 8 is not divisible by 3.
a(3) = 15, since 15 = 3*5 has 2 prime factors and 15 is not divisible by 2.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..10000
• Paul Erdős and Carl Pomerance, On a theorem of Besicovitch: values of arithmetic functions that divide their arguments, Indian J. Math., Vol. 32 (1990), pp. 279-287.

Crossrefs

Cf. A000040, A001222, A074946 (complement), A100118, A046363, A133620, A133621.

Cf. A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134335, A134344, A134376.

Programs

Mathematica

Select[Range[2,200],Mod[#,PrimeOmega[#]]!=0&] (* Harvey P. Dale, May 13 2023 *)

PARI

isok(n) = (n % bigomega(n)) \\ Michel Marcus, Jul 15 2013