A374034 a(n) = A276150(gcd(A276085(n), A328768(n))), where A276150 is the digit sum in primorial base, A276085 is the primorial base log-function, and A328768 is the first primorial based variant of arithmetic derivative.

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 4, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 6, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3

Offset: 1

Author

Antti Karttunen, Jun 27 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for sequences related to primorial numbers

Crossrefs

Cf. A002110, A276085, A276150, A328768, A374031.

Cf. also A328771, A373989.

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)); };
A276150(n) = { my(s=0, p=2, d); while(n, d = (n%p); s += d; n = (n-d)/p; p = nextprime(1+p)); (s); };
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]));
A374034(n) = A276150(gcd(A276085(n), A328768(n)));

Formula

a(n) = A276150(A374031(n)).

Apparently, a(n) <= A328771(n) for all n >= 1.