A356304 The least k >= 0 such that A003415(n) and A276086(n+k) are relatively prime, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 0, 0, 0, 24, 0, 4, 3, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 4, 9, 0, 0, 0, 5, 4, 3, 0, 0, 0, 0, 0, 177, 0, 1, 24, 0, 172, 1, 0, 0, 0, 0, 4, 3, 14, 0, 162, 161, 10, 9, 158, 0, 0, 1, 0, 1, 0, 0, 0, 0, 4, 3, 2, 1, 0, 0, 4, 1, 0, 0, 0, 0, 4, 15, 14, 1, 0, 0, 0, 3, 0, 0, 0, 1, 4, 1, 122, 0, 0, 1, 4, 1, 116, 1, 0, 0, 2212, 21

Offset

2,5

Links

Antti Karttunen, Table of n, a(n) for n = 2..11550

Antti Karttunen, Data supplement: n, a(n) computed for n = 2..65537

Index entries for sequences related to primorial base

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); };
A356304(n) = { my(k=0, x=A003415(n)); while(gcd(A276086(n+k), x)!=1, k++); (k); };

Crossrefs

Cf. A003415, A276086, A356311 (after its initial zero gives the positions of zeros in this sequence).

Cf. also A356302, A356305.

Sequence in context: A353227 A075406 A075404 * A308234 A362795 A242837

Adjacent sequences: A356301 A356302 A356303 * A356305 A356306 A356307

Keyword

nonn

Author

Antti Karttunen, Nov 03 2022

Status

approved