|
%I #24 Jul 06 2024 14:02:30
%S 0,1,0,0,0,-1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,0,1,0,0,
%T 0,-1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,-1,0,0,
%U 0,1,0,0,0,1,0,0,0,-1,0,0,0,1,0,0,0,-1,0,0,0,-1,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,1,0,0,0
%N For odd n: a(n) = 0, and for even n: a(n) = -mu(n), where mu is Moebius function (A008683).
%C Sum of Möbius function values computed for terms of 3x+1 trajectory started at n, but excluding mu(n) itself. See _Marc LeBrun_'s comment in A087003.
%H Antti Karttunen, <a href="/A292273/b292273.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F a(n) = (A000035(n)-1) * A008683(n).
%F a(n) = A087003(n) - A008683(n).
%F Conjecture: a(n) = Re(A008683(n)*(i^n)). - _Mats Granvik_, Jul 06 2024
%o (PARI)
%o A292273(n) = if(n%2, 0, -moebius(n)); \\ After the definition.
%o \\ Implementation following the Collatz-interpretation:
%o A006370(n) = if(n%2, 3*n+1, n/2); \\ This function from _Michael B. Porter_, May 29 2010
%o A087003(n) = { my(s=1); while(n>1, s += moebius(n); n = A006370(n)); (s); };
%o A292273(n) = (A087003(n)-moebius(n));
%o \\ Or more directly as:
%o A292273(n) = { my(s=0); while(n>1, n = A006370(n); s += moebius(n)); (s); };
%o (Scheme) (define (A292273 n) (* (- (A000035 n) 1) (A008683 n)))
%Y Cf. A000035, A006370, A008683, A014682, A039956 (positions of nonzero terms), A087003.
%K sign,easy
%O 1
%A _Antti Karttunen_, Sep 14 2017
|
