A369669 The greatest common divisor of the first and the second arithmetic derivative of n.

0, 0, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 16, 1, 3, 4, 16, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 27, 16, 1, 1, 1, 16, 1, 1, 4, 4, 1, 1, 16, 4, 1, 1, 1, 16, 1, 5, 1, 16, 1, 3, 4, 4, 1, 27, 16, 4, 1, 1, 1, 4, 1, 1, 1, 64, 3, 1, 1, 12, 1, 1, 1, 4, 1, 1, 1, 16, 3, 1, 1, 16, 108, 1, 1, 4, 1, 3, 16, 4, 1, 1, 4, 16, 1, 7, 4, 16, 1, 1, 5

Offset: 0

Author

Antti Karttunen, Feb 10 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A068346, A085731, A370130 [= a(A276086(n))].

Cf. A328393 (positions of 1's), A354874 (their characteristic function).

Cf. A327864 (positions of even terms, also positions of multiples of 4).

Cf. A370119 (positions of multiples of 3).

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369669(n) = { my(d=A003415(n)); gcd(d, A003415(d)); };

Formula

a(n) = gcd(A003415(n), A068346(n)).

For n >= 2, a(n) = A085731(A003415(n)).