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

0, 0, 3, 6, 36, 18, 5, 10, 60, 30, 315, 90, 400, 50, 225, 600, 7200, 450, 2625, 250, 3000, 750, 14625, 2250, 27500, 1250, 1875, 33750, 180000, 11250, 217, 14, 1680, 42, 1197, 252, 420, 70, 105, 1680, 21420, 630, 7175, 350, 8400, 13650, 1575, 3150, 14000, 1750, 7875, 10500, 63000, 15750, 354375, 70000

Offset: 0

Author

Antti Karttunen, Jan 02 2023

Keywords

• nonn
• base

Examples

			For n=32, we have A003415(32) = 80 and A276086(32) = 21, therefore a(32) = lcm(80,21) = 1680.
For n=39, we have A003415(39) = 16 and A276086(39) = 210, therefore a(39) = lcm(16,210) = 1680.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327858, A358669, A359424 [= a(n) mod 60].

Cf. A016825 (positions of odd terms), A042965 (of even terms), A327864 (of multiples of 4).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A359423(n) = lcm(A003415(n), A276086(n));

Formula

a(n) = lcm(A003415(n), A276086(n)).

a(n) = A358669(n) / A327858(n).