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

1,1

Comments

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

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.

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A306490 A256351 A050688 * A351048 A292188 A301659

Adjacent sequences: A134331 A134332 A134333 * A134335 A134336 A134337

Keyword

nonn

Author

Hieronymus Fischer, Oct 23 2007

Status

approved