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A359423 The least common multiple of the arithmetic derivative and the primorial base exp-function.

%I A359423 #10 Jan 02 2023 21:55:50
%S A359423 0,0,3,6,36,18,5,10,60,30,315,90,400,50,225,600,7200,450,2625,250,
%T A359423 3000,750,14625,2250,27500,1250,1875,33750,180000,11250,217,14,1680,
%U A359423 42,1197,252,420,70,105,1680,21420,630,7175,350,8400,13650,1575,3150,14000,1750,7875,10500,63000,15750,354375,70000
%N A359423 The least common multiple of the arithmetic derivative and the primorial base exp-function.
%H A359423 Antti Karttunen, <a href="/A359423/b359423.txt">Table of n, a(n) for n = 0..11550</a>
%H A359423 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A359423 a(n) = lcm(A003415(n), A276086(n)).
%F A359423 a(n) = A358669(n) / A327858(n).
%e A359423 For n=32, we have A003415(32) = 80 and A276086(32) = 21, therefore a(32) = lcm(80,21) = 1680.
%e A359423 For n=39, we have A003415(39) = 16 and A276086(39) = 210, therefore a(39) = lcm(16,210) = 1680.
%o A359423 (PARI)
%o A359423 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A359423 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A359423 A359423(n) = lcm(A003415(n), A276086(n));
%Y A359423 Cf. A003415, A276086, A327858, A358669, A359424 [= a(n) mod 60].
%Y A359423 Cf. A016825 (positions of odd terms), A042965 (of even terms), A327864 (of multiples of 4).
%K A359423 nonn,base
%O A359423 0,3
%A A359423 _Antti Karttunen_, Jan 02 2023