A300824 Difference between A300222(n) and its Möbius transform.

0, 0, 0, 2, 0, 2, 0, 0, 0, 4, 0, 4, 0, 8, 2, 8, 0, 6, 0, -2, 6, 4, 0, 8, 2, 2, 0, 0, 0, 8, 0, 6, 2, 10, 8, 12, 0, 20, 0, 28, 0, 18, 0, 16, 6, 22, 0, 22, 6, 22, 8, 24, 0, 18, 4, 8, 18, 4, 0, 16, 0, 2, 18, 2, 2, 26, 0, 4, 20, 0, 0, 24, 0, 2, 28, 0, 8, 30, 0, -2, 0, 4, 0, 0, 10, 8, 2, 16, 0, 24, 6, 16, 0, 22, 20, 14, 0, 14, 6, 40, 0, 26, 0, 32, 24

Offset: 1

Author

Antti Karttunen, Mar 14 2018

Keywords

• sign
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A008683, A051953, A300222, A300822, A300823, A300825.

Programs

Mathematica

f[n_] := FromDigits[IntegerDigits[n, 3] /. 1 -> 0, 3]; Table[f@ n - DivisorSum[n, MoebiusMu[n/#] f@ # &], {n, 105}] (* Michael De Vlieger, Mar 17 2018 *)

PARI

A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
A300824(n) = -sumdiv(n,d,(dA300222(d));

Formula

a(n) = A300222(n) - A300822(n).

a(n) = -Sum_{d|n, dA008683(n/d)*A300222(d) = Sum_{d|n, dA300822(d).

a(n) = A051953(n) - A300823(n).