A297112 Möbius transform of A156552.

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

Offset: 1

Author

Antti Karttunen, Dec 26 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A008683, A064989, A156552, A297113.

Cf. also A297106, A297156, A297171, A297172.

Programs

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

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).