A368921 a(n) = n' - n'', where n' is the arithmetic derivative of n, A003415(n) and n'' is its second arithmetic derivative, A068346(n).

0, 0, 1, 1, 0, 1, 4, 1, -4, 1, 6, 1, -16, 1, 3, -4, -48, 1, 11, 1, -20, 3, 12, 1, -4, 3, 7, 0, -48, 1, 30, 1, -96, 5, 18, -4, -32, 1, 11, -16, -4, 1, 40, 1, -64, 23, 15, 1, -128, 5, 6, -4, -36, 1, -27, -16, -4, 9, 30, 1, -4, 1, 19, 31, -448, -3, 60, 1, -84, 11, 58, 1, -64, 1, 23, 39, -96, -3, 70, 1, -192, -108, 42

Offset: 0

Author

Antti Karttunen, Jan 10 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A003415, A068346, A348329 (positions of 0's), A368922.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A368921(n) = { my(u=A003415(n)); (u-A003415(u)); };

Formula

a(n) = A003415(n) - A068346(n).

a(n) = A368922(n) + A068346(n).