A370120 a(n) = A276085(A370117(n)), where A370117(n) is the denominator of n/A276086(A003415(n)), A003415 is the arithmetic derivative, A276086 is the primorial base exp-function, and A276085 is its inverse, the primorial base log-function.

0, 0, 0, 1, 4, 1, 2, 1, 12, 6, 0, 1, 14, 1, 8, 0, 32, 1, 18, 1, 18, 8, 12, 1, 42, 4, 14, 25, 2, 1, 30, 1, 80, 12, 18, 6, 60, 1, 20, 14, 62, 1, 8, 1, 48, 31, 24, 1, 110, 14, 32, 18, 56, 1, 78, 10, 62, 20, 30, 1, 90, 1, 32, 19, 192, 12, 60, 1, 72, 24, 22, 1, 156, 1, 38, 43, 80, 18, 68, 1, 170, 108, 42, 1, 92, 16, 44

Offset: 0

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16384

Crossrefs

Cf. A003415, A276085, A276086, A327859, A369964, A370115 (positions of 0's), A370117.

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)); };
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); };
A370120(n) = { my(u=A276086(A003415(n))); A276085(u/gcd(n, u)); };

Formula

a(n) = A276085(A370117(n)).