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

1,8

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to primorial numbers

Formula

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

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

Prog

(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)));

Crossrefs

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

Cf. also A328771, A373989.

Sequence in context: A225518 A269972 A202205 * A336123 A353849 A075661

Adjacent sequences: A374031 A374032 A374033 * A374035 A374036 A374037

Keyword

nonn

Author

Antti Karttunen, Jun 27 2024

Status

approved