A370117 Denominator of n/A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

1, 1, 1, 2, 9, 2, 3, 2, 25, 5, 1, 2, 75, 2, 15, 1, 21, 2, 125, 2, 125, 15, 25, 2, 175, 9, 75, 1250, 3, 2, 7, 2, 18375, 25, 125, 5, 49, 2, 375, 75, 147, 2, 15, 2, 875, 14, 625, 2, 128625, 75, 21, 125, 13125, 2, 6125, 45, 147, 375, 7, 2, 343, 2, 21, 250, 2941225, 25, 49, 2, 1225, 625, 1125, 2, 84035, 2, 105, 350

Offset: 0

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn
• frac

Comments

Sequence contains only terms of A048103.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A003415, A276086, A327859, A369964, A370115 (positions of 1's), A370116 (numerators), A370120.

Programs

PARI

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); };
A370117(n) = { my(u=A276086(A003415(n))); (u/gcd(n, u)); };

Formula

a(n) = A327859(n) / A369964(n) = A327859(n) / gcd(n, A276086(A003415(n))).

a(n) = A276086(A370120(n)).