A368922 a(n) = n' - n''*2, where n' is the arithmetic derivative of n, A003415(n) and n'' is the second arithmetic derivative, A068346(n).

0, 0, 1, 1, -4, 1, 3, 1, -20, -4, 5, 1, -48, 1, -3, -16, -128, 1, 1, 1, -64, -4, 11, 1, -52, -4, -1, -27, -128, 1, 29, 1, -272, -4, 17, -20, -124, 1, 1, -48, -76, 1, 39, 1, -176, 7, 5, 1, -368, -4, -33, -28, -128, 1, -135, -48, -100, -4, 29, 1, -100, 1, 5, 11, -1088, -24, 59, 1, -240, -4, 57, 1, -284, 1, 7, 23, -272

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, A334261 (positions of -4's), A368701, A368921.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A368922(n) = { my(u=A003415(n)); (u-2*A003415(u)); };

Formula

a(n) = A003415(n) - 2*A068346(n).

a(n) = A368921(n) - A068346(n).