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A297112
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Möbius transform of A156552.
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21
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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
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OFFSET
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1,3
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..2048
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FORMULA
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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).
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Dec 26 2017
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STATUS
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approved
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