cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A134334 #18 May 13 2023 13:12:05
%S A134334 8,9,15,20,21,25,28,32,33,35,39,44,48,49,50,51,52,54,55,57,64,65,68,
%T A134334 69,70,72,76,77,81,85,87,90,91,92,93,95,98,108,110,111,112,115,116,
%U A134334 119,121,123,124,125,126,128,129,130,133,135,141,143,145,148,150,154,155,159
%N A134334 Numbers which are not divisible by the number of their prime factors (counted with multiplicity).
%C A134334 The asymptotic density of this sequence is 1 (Erdős and Pomerance, 1990). - _Amiram Eldar_, Jul 10 2020
%H A134334 Hieronymus Fischer, <a href="/A134334/b134334.txt">Table of n, a(n) for n = 1..10000</a>
%H A134334 Paul Erdős and Carl Pomerance, <a href="https://math.dartmouth.edu/~carlp/PDF/paper79.pdf">On a theorem of Besicovitch: values of arithmetic functions that divide their arguments</a>, Indian J. Math., Vol. 32 (1990), pp. 279-287.
%e A134334 a(1) = 8, since 8 = 2*2*2 has 3 prime factors and 8 is not divisible by 3.
%e A134334 a(3) = 15, since 15 = 3*5 has 2 prime factors and 15 is not divisible by 2.
%t A134334 Select[Range[2,200],Mod[#,PrimeOmega[#]]!=0&] (* _Harvey P. Dale_, May 13 2023 *)
%o A134334 (PARI) isok(n) = (n % bigomega(n)) \\ _Michel Marcus_, Jul 15 2013
%Y A134334 Cf. A000040, A001222, A074946 (complement), A100118, A046363, A133620, A133621.
%Y A134334 Cf. A133880, A133890, A133900, A133910, A133911, A046346, A134331, A134332, A134333, A134335, A134344, A134376.
%K A134334 nonn
%O A134334 1,1
%A A134334 _Hieronymus Fischer_, Oct 23 2007