A328382 a(n) = A276086(n) mod A003415(n), where A276086 is the primorial base exp-function and A003415 is the arithmetic derivative.

0, 0, 1, 0, 0, 0, 3, 0, 3, 0, 9, 0, 3, 6, 1, 0, 20, 0, 15, 0, 7, 0, 9, 0, 0, 24, 25, 0, 7, 0, 21, 0, 6, 6, 35, 0, 0, 2, 43, 0, 11, 0, 45, 36, 0, 0, 91, 0, 15, 10, 35, 0, 1, 14, 61, 4, 5, 0, 49, 0, 15, 39, 57, 0, 1, 0, 15, 14, 22, 0, 133, 0, 9, 35, 65, 0, 19, 0, 71, 30, 42, 0, 121, 2, 30, 6, 105, 0, 97, 6, 69, 18, 0, 6, 83, 0, 63, 15, 35, 0, 21

Offset: 2

Author

Antti Karttunen, Oct 15 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327858, A358220, A358221 (positions of 0's), A358232 (of 1's), A358228 (of odd terms), A358229 (of even terms), A358227 (parity of terms).

Cf. also A328386.

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); };
A328382(n) = (A276086(n)%A003415(n));

Formula

a(n) = A276086(n) mod A003415(n).

For n >= 2, gcd(a(n), A003415(n)) = A327858(n).