A351232 a(n) = floor(A276086(n) / A003415(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

3, 6, 2, 18, 1, 10, 1, 5, 6, 90, 1, 50, 8, 18, 7, 450, 5, 250, 15, 75, 86, 2250, 14, 125, 125, 138, 175, 11250, 0, 14, 0, 3, 3, 10, 0, 70, 5, 13, 4, 630, 4, 350, 10, 26, 63, 3150, 7, 125, 58, 262, 140, 15750, 54, 546, 142, 1193, 1270, 78750, 0, 98, 4, 5, 2, 49, 4, 490, 10, 56, 37, 4410, 7, 2450, 94, 133, 137, 1225

Offset: 2

Author

Antti Karttunen, Feb 05 2022

Keywords

• nonn
• base
• easy
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 2..11050
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A351230, A351231.

Cf. A351228 (conjectured to give the positions of zeros from its second term onward).

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); };
A351232(n) = floor(A276086(n) / A003415(n));

Formula

a(n) = floor(A276086(n) / A003415(n)) = floor(A351231(n) / A351230(n)).