A369038 Numerator of ratio A003415(n) / A003415(A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

0, 1, 1, 2, 1, 5, 1, 3, 6, 7, 1, 8, 1, 9, 8, 2, 1, 7, 1, 12, 2, 13, 1, 11, 2, 3, 27, 16, 1, 31, 1, 8, 14, 19, 4, 5, 1, 21, 16, 34, 1, 41, 1, 12, 39, 5, 1, 56, 14, 9, 4, 14, 1, 27, 16, 46, 22, 31, 1, 46, 1, 33, 51, 16, 6, 61, 1, 36, 26, 59, 1, 13, 1, 39, 1, 8, 6, 71, 1, 11, 108, 43, 1, 62, 22, 9, 32, 1, 1, 41, 20

Offset: 1

Author

Antti Karttunen, Jan 20 2024

Keywords

• nonn
• frac
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A003415, A276086, A327860, A345000, A369039 (denominators).

Cf. also A351230, A351250.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A327860(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= (p^e); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
A369038(n) = { my(u=A003415(n)); (u/gcd(u,A327860(n))); };

Formula

a(n) = A003415(n) / A345000(n) = A003415(n) / gcd(A003415(n), A327860(n)).