A300823 Difference between A244042 and its Möbius transform.

0, 1, 1, 0, 1, 2, 1, 4, 3, 2, 1, 4, 1, 0, 5, 0, 1, 6, 1, 14, 3, 8, 1, 8, 3, 12, 9, 16, 1, 14, 1, 10, 11, 8, 3, 12, 1, 0, 15, -4, 1, 12, 1, 8, 15, 2, 1, 10, 1, 8, 11, 4, 1, 18, 11, 24, 3, 26, 1, 28, 1, 30, 9, 30, 15, 20, 1, 32, 5, 46, 1, 24, 1, 36, 7, 40, 9, 24, 1, 50, 27, 38, 1, 60, 11, 36, 29, 32, 1, 42, 13, 32, 33, 26, 3, 50, 1

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, A244042, A300821, A300824, A300825.

Programs

Mathematica

f[n_] := FromDigits[IntegerDigits[n, 3] /. 2 -> 0, 3]; Table[f@ n - DivisorSum[n, MoebiusMu[n/#] f@ # &], {n, 97}] (* Michael De Vlieger, Mar 17 2018 *)

PARI

A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300823(n) = -sumdiv(n,d,(dA244042(d));

Formula

a(n) = A244042(n) - A300821(n).

a(n) = -Sum_{d|n, dA008683(n/d)*A244042(d) = Sum_{d|n, dA300821(d).

a(n) = A051953(n) - A300824(n).