A356305 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, 1, 0, 0, 0, 0, 1, 0, 2, 3, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 17, 0, 0, 0, 21, 25, 2, 0, 0, 0, 0, 0, 5, 0, 5, 6, 0, 13, 1, 0, 0, 0, 0, 2, 2, 11, 0, 20, 21, 19, 17, 24, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 4, 5, 0, 0, 2, 1, 0, 0, 0, 0, 1, 10, 12, 5, 0, 0, 0, 3, 0, 0, 0, 1, 25, 1, 84, 0, 0, 1, 2, 1, 65, 5, 0, 0, 69, 8, 96

Offset: 0

Author

Antti Karttunen, Nov 03 2022

Keywords

• nonn
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 0..11550
• Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A356311 (positions of 0's).

Cf. also A356303, A356304.

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); };
A356305(n) = { my(k=0,x=A003415(n)); while(gcd(A276086(n-k),x)!=1,k++); (k); };