A370116 Numerator of n/A276086(A003415(n)), where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

0, 1, 1, 3, 4, 5, 1, 7, 8, 9, 1, 11, 4, 13, 7, 1, 16, 17, 3, 19, 4, 7, 11, 23, 8, 5, 13, 9, 4, 29, 15, 31, 32, 11, 17, 7, 36, 37, 19, 13, 8, 41, 1, 43, 44, 3, 23, 47, 16, 49, 1, 17, 52, 53, 9, 11, 8, 19, 29, 59, 20, 61, 31, 3, 64, 13, 33, 67, 68, 23, 1, 71, 72, 73, 37, 3, 76, 77, 13, 79, 16, 81, 41, 83, 4, 17, 43

Offset: 0

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn
• frac

Links

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

Crossrefs

Cf. A003415, A276086, A327859, A369964, A370114 (positions of 1's), A370117 (denominators).

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); };
A370116(n) = (n/gcd(n, A276086(A003415(n))));

Formula

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