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

2,7

Links

Antti Karttunen, Table of n, a(n) for n = 2..30030

Index entries for sequences related to primorial base

Formula

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

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

Prog

(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));

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.

Sequence in context: A356169 A055945 A138123 * A211868 A127372 A350950

Adjacent sequences: A328379 A328380 A328381 * A328383 A328384 A328385

Keyword

nonn

Author

Antti Karttunen, Oct 15 2019

Status

approved