A297171 Möbius transform of A243071.

0, 1, 3, 1, 7, 2, 15, 2, 2, 6, 31, 5, 63, 14, 3, 4, 127, 2, 255, 13, 11, 30, 511, 10, 4, 62, 4, 29, 1023, 4, 2047, 8, 27, 126, 5, 4, 4095, 254, 59, 26, 8191, 12, 16383, 61, 10, 510, 32767, 20, 8, 4, 123, 125, 65535, 4, 21, 58, 251, 1022, 131071, 7, 262143, 2046, 26, 16, 53, 28, 524287, 253, 507, 6, 1048575, 8

Offset

1,3

Links

Antti Karttunen, Table of n, a(n) for n = 1..4096

Formula

a(n) = Sum_{d|n} A008683(n/d)*A243071(d).

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)};
A243071(n) = if(n<=2, n-1, if(!(n%2), 2*A243071(n/2), 1+(2*A243071(A064989(n)))));
A297171(n) = sumdiv(n, d, moebius(n/d)*A243071(d));

Crossrefs

Cf. A008683, A064989, A243071, A297161 (rgs-transform of this sequence).

Cf. also A297112, A297156, A297172.

Sequence in context: A065289 A065265 A235263 * A297156 A132885 A187818

Adjacent sequences: A297168 A297169 A297170 * A297172 A297173 A297174

Keyword

nonn

Author

Antti Karttunen, Dec 26 2017

Status

approved