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

0,5

Links

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

Formula

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

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

Prog

(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)); };

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).

Sequence in context: A234957 A327939 A365837 * A155826 A273711 A340227

Adjacent sequences: A369666 A369667 A369668 * A369670 A369671 A369672

Keyword

nonn

Author

Antti Karttunen, Feb 10 2024

Status

approved