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A383299 Numbers k such that A276086(k) is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A383299 #16 Jul 08 2025 07:52:05
%S A383299 0,1,3,4,5,7,9,11,13,15,17,19,23,27,29,31,37,41,43,45,47,51,53,59,61,
%T A383299 67,71,73,79,83,87,89,97,101,103,107,109,113,117,119,127,131,137,139,
%U A383299 141,147,149,151,157,161,163,165,167,171,173,177,179,181,191,193,197,199,203,207,209,211,223,227,229,233,239
%N A383299 Numbers k such that A276086(k) is a multiple of A276086(A003415(k)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%C A383299 The sequence contains the intersection of A048103, A369650, and A328387. That is, {1, 15, 5005}, at least.
%H A383299 Antti Karttunen, <a href="/A383299/b383299.txt">Table of n, a(n) for n = 1..20000</a>
%H A383299 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e A383299 5 is a term as A003415(5) = 1, and A276086(5) = 18 is a multiple of A276086(1) = 2, and ditto for all odd primes.
%e A383299 9 is a term as A003415(9) = 6, and A276086(9) = 30 is a multiple of A276086(6) = 5.
%e A383299 15 is a term as A003415(15) = 8, and A276086(15) = 150 is a multiple of A276086(8) = 15.
%e A383299 5005 is a term as A003415(5005) = 2556, and A276086(5005) = 39055266250 = 7803250 * A276086(2556) = 7803250 * 5005. See also A369650.
%e A383299 See also examples in A383300.
%o A383299 (PARI) isA383299 = A383298;
%Y A383299 Cf. A003415, A048103, A276086, A327859, A328387, A383298 (characteristic function).
%Y A383299 Cf. A006005, A051674, A383300, A383301 (subsequences).
%Y A383299 Cf. also A369650.
%K A383299 nonn
%O A383299 1,3
%A A383299 _Antti Karttunen_, May 15 2025