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

1,6

Links

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

Formula

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

a(n) = -Sum_{d|n, d<n} A008683(n/d)*A244042(d) = Sum_{d|n, d<n} A300821(d).

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

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 *)

Prog

(PARI)
A244042(n) = fromdigits(apply(x->(x%2), digits(n, 3)), 3);
A300823(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A244042(d));

Crossrefs

Cf. A008683, A051953, A244042, A300821, A300824, A300825.

Sequence in context: A109977 A201199 A318459 * A345942 A175702 A303781

Adjacent sequences: A300820 A300821 A300822 * A300824 A300825 A300826

Keyword

sign,base

Author

Antti Karttunen, Mar 14 2018

Status

approved