A369052 a(n) = n - n'*2, where n' is the arithmetic derivative of n, A003415.

0, 1, 0, 1, -4, 3, -4, 5, -16, -3, -4, 9, -20, 11, -4, -1, -48, 15, -24, 17, -28, 1, -4, 21, -64, 5, -4, -27, -36, 27, -32, 29, -128, 5, -4, 11, -84, 35, -4, 7, -96, 39, -40, 41, -52, -33, -4, 45, -176, 21, -40, 11, -60, 51, -108, 23, -128, 13, -4, 57, -124, 59, -4, -39, -320, 29, -56, 65, -76, 17, -48, 69, -240, 71

Offset: 0

Author

Antti Karttunen, Jan 17 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A003415.

Cf. also A068719, A168036, A368921, A368922.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369052(n) = (n-2*A003415(n));

Formula

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

a(n) = -(A003415(n)+A168036(n)).