A374031 a(n) = gcd(A276085(n), A328768(n)), where A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.

0, 1, 2, 2, 6, 1, 30, 3, 4, 1, 210, 4, 2310, 1, 4, 4, 30030, 1, 510510, 4, 8, 1, 9699690, 1, 12, 1, 6, 4, 223092870, 1, 6469693230, 5, 4, 1, 12, 6, 200560490130, 1, 4, 9, 7420738134810, 1, 304250263527210, 4, 2, 1, 13082761331670030, 2, 60, 1, 4, 4, 614889782588491410, 1, 36, 3, 16, 1, 32589158477190044730, 2

Offset: 1

Author

Antti Karttunen, Jun 26 2024

Keywords

• nonn

Links

• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A276085, A328768, A374042 (positions of multiples of 3).

Programs

PARI

A002110(n) = prod(i=1,n,prime(i));
A276085(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*A002110(primepi(f[k, 1])-1)); };
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i,1])-1)/f[i, 1]));
A374031(n) = gcd(A276085(n), A328768(n));