|
|
A229344
|
|
Mertens's function of the arithmetic derivative of n: a(n) = M(n'), a(1) = 0.
|
|
3
|
|
|
0, 1, 1, -1, 1, -2, 1, -2, -1, -2, 1, -1, 1, -2, -2, -4, 1, -2, 1, -2, -1, -3, 1, -3, -1, -1, -1, -4, 1, -4, 1, -4, -2, -3, -2, -1, 1, -2, -1, -2, 1, -1, 1, -3, 0, -2, 1, -4, -2, -3, -3, -2, 1, -4, -1, -1, -1, -4, 1, -1, 1, -3, -2, -5, -2, -2, 1, -3, -1, -1, 1, -1, 1, 0, -2, -4, -2, -3, 1, -4, -3, -3, 1, -1, -1, -3, -4, -4, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
For n=4, M(n') = M(4') = M(4) = -1.
For n=7, M(n') = M(7') = M(1) = 1.
|
|
MATHEMATICA
|
Array[Total@ Map[MoebiusMu, Range@ If[Abs@ # < 2, 0, # Total[#2/#1 & @@@ FactorInteger[Abs@ #]]]] &, 89] (* Michael De Vlieger, Nov 01 2017 *)
|
|
PROG
|
(PARI) rd(n) = {local(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]; )); }
(PARI)
A002321(n) = sum(k=1, n, moebius(k));
A003415(n) = { my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From Michael B. Porter, Nov 25 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Description and formula clarified and more terms added by Antti Karttunen, Nov 01 2017
|
|
STATUS
|
approved
|
|
|
|