A369039 Denominator of ratio A003415(n) / A003415(A276086(n)), where A003415 is the arithmetic derivative and A276086 is the primorial base exp-function.

1, 1, 5, 3, 21, 1, 7, 2, 31, 39, 123, 5, 45, 55, 185, 15, 705, 25, 275, 175, 215, 1425, 3975, 125, 325, 425, 6125, 4125, 22125, 1, 9, 1, 41, 51, 55, 1, 59, 71, 247, 159, 951, 95, 365, 115, 1445, 381, 5385, 325, 2175, 565, 1655, 2775, 30075, 1375, 12625, 8375, 46625, 63375, 166125, 7, 77, 91, 329, 35, 427, 119, 483

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, A369038 (numerators).

Cf. also A351231, A351251.

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); };
A369039(n) = { my(u=A327860(n)); u/gcd(A003415(n),u); };

Formula

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