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A373992 Numbers k such that A328768(k) is a multiple of 3, where A328768 is the first primorial based variant of arithmetic derivative.

%I A373992 #23 Jun 28 2024 04:52:09
%S A373992 0,1,5,7,8,9,11,13,17,18,19,23,25,27,29,31,35,36,37,40,41,43,45,47,49,
%T A373992 53,54,55,56,59,61,63,64,65,67,71,72,73,77,79,81,83,85,88,89,90,91,95,
%U A373992 97,99,101,103,104,107,108,109,113,115,117,119,121,125,126,127,131,133,135,136,137,139,143,144,145,149
%N A373992 Numbers k such that A328768(k) is a multiple of 3, where A328768 is the first primorial based variant of arithmetic derivative.
%C A373992 Term is present if and only if it is either a multiple of 9, or it is not a multiple of 3 but its 2-adic valuation is (a multiple of 3).
%C A373992 A multiplicative semigroup: if m and n are in the sequence, then so is m*n.
%C A373992 The asymptotic density of this sequence is 31/63. - _Amiram Eldar_, Jun 28 2024
%H A373992 Antti Karttunen, <a href="/A373992/b373992.txt">Table of n, a(n) for n = 1..12000</a>
%H A373992 <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>.
%t A373992 Select[Range[0, 150], Divisible[#, 9] || (!Divisible[#, 3] && Divisible[IntegerExponent[#, 2], 3]) &] (* _Amiram Eldar_, Jun 28 2024 *)
%o A373992 (PARI) isA373992 = A373991;
%Y A373992 Cf. A328768, A373991 (characteristic function).
%Y A373992 Union of A008591 and A374044.
%Y A373992 Cf. A374042 (subsequence).
%Y A373992 Cf. also A042965 (where A328768 is a multiple of 2), A327863 (where A003415 is a multiple of 3).
%K A373992 nonn,easy
%O A373992 1,3
%A A373992 _Antti Karttunen_, Jun 26 2024