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A292273 For odd n: a(n) = 0, and for even n: a(n) = -mu(n), where mu is Moebius function (A008683). 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

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.

LINKS

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

Index entries for sequences related to 3x+1 (or Collatz) problem

FORMULA

a(n) = (A000035(n)-1) * A008683(n).

a(n) = A087003(n) - A008683(n).

PROG

(PARI)

A292273(n) = if(n%2, 0, -moebius(n)); \\ After the definition.

\\ Implementation following the Collatz-interpretation:

A006370(n) = if(n%2, 3*n+1, n/2); \\ This function from Michael B. Porter, May 29 2010

A087003(n) = { my(s=1); while(n>1, s += moebius(n); n = A006370(n)); (s); };

A292273(n) = (A087003(n)-moebius(n));

\\ Or more directly as:

A292273(n) = { my(s=0); while(n>1, n = A006370(n); s += moebius(n)); (s); };

(Scheme) (define (A292273 n) (* (- (A000035 n) 1) (A008683 n)))

CROSSREFS

Cf. A000035, A006370, A008683, A014682, A039956 (positions of nonzero terms), A087003.

Sequence in context: A284745 A241666 A285957 * A285949 A285530 A317542

Adjacent sequences:  A292270 A292271 A292272 * A292274 A292275 A292276

KEYWORD

sign

AUTHOR

Antti Karttunen, Sep 14 2017

STATUS

approved

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Last modified December 17 04:31 EST 2018. Contains 318192 sequences. (Running on oeis4.)