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A300824
Difference between A300222(n) and its Möbius transform.
5
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
1,4
LINKS
FORMULA
a(n) = A300222(n) - A300822(n).
a(n) = -Sum_{d|n, d<n} A008683(n/d)*A300222(d) = Sum_{d|n, d<n} A300822(d).
a(n) = A051953(n) - A300823(n).
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 *)
PROG
(PARI)
A300222(n) = fromdigits(apply(x->(if (1==x, 0, x)), digits(n, 3)), 3);
A300824(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A300222(d));
CROSSREFS
KEYWORD
sign,base
AUTHOR
Antti Karttunen, Mar 14 2018
STATUS
approved