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A297112 Möbius transform of A156552. 21
0, 1, 2, 2, 4, 2, 8, 4, 4, 4, 16, 4, 32, 8, 4, 8, 64, 4, 128, 8, 8, 16, 256, 8, 8, 32, 8, 16, 512, 4, 1024, 16, 16, 64, 8, 8, 2048, 128, 32, 16, 4096, 8, 8192, 32, 8, 256, 16384, 16, 16, 8, 64, 64, 32768, 8, 16, 32, 128, 512, 65536, 8, 131072, 1024, 16, 32, 32, 16, 262144, 128, 256, 8, 524288, 16, 1048576, 2048, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2048

FORMULA

a(1) = 0, a(2) = 1, after which, a(2n+1) = 2*a(A064989(2n+1)), a(4n) = 2*a(2n), a(4n+2) = a(2n+1).

a(n) = Sum_{d|n} A008683(n/d)*A156552(d).

For n > 1, a(n) = A000079(A297113(n)-1).

PROG

(PARI)

A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};

A156552(n) = if(1==n, 0, if(!(n%2), 1+(2*A156552(n/2)), 2*A156552(A064989(n))));

A297112(n) = sumdiv(n, d, moebius(n/d)*A156552(d));

(Scheme, with memoization-macro definec) (definec (A297112 n) (cond ((<= n 2) (- n 1)) ((odd? n) (* 2 (A297112 (A064989 n)))) ((= 2 (modulo n 4)) (A297112 (/ n 2))) (else (* 2 (A297112 (/ n 2)))))) ;; Antti Karttunen, Dec 27 2017

CROSSREFS

Cf. A008683, A064989, A156552, A297113.

Cf. also A297106, A297156, A297171, A297172.

Sequence in context: A200147 A235063 A084540 * A259192 A131999 A113416

Adjacent sequences:  A297109 A297110 A297111 * A297113 A297114 A297115

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 26 2017

STATUS

approved

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Last modified February 22 05:17 EST 2019. Contains 320385 sequences. (Running on oeis4.)