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

Author

Antti Karttunen, Nov 03 2022

Keywords

• nonn

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

Crossrefs

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

Cf. also A356302, A356305.

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